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Volumn 124, Issue 1, 1996, Pages 27-79

The characterization of reaction-convection-diffusion processes by travelling waves

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EID: 0029703999     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1996.0002     Document Type: Article
Times cited : (58)

References (173)
  • 2
    • 0000836987 scopus 로고
    • Quasilinear elliptic-parabolic differential equations
    • 2. H. W. ALT AND S. LUCKHAUS, Quasilinear elliptic-parabolic differential equations, Math. Z. 183 (1983), 311-341.
    • (1983) Math. Z. , vol.183 , pp. 311-341
    • Alt, H.W.1    Luckhaus, S.2
  • 3
    • 0011668454 scopus 로고
    • On the initial growth of the interfaces in nonlinear diffusion-convection processes
    • (W.-M. Ni, L. A. Peletier, and J. Serrin, Eds.), Springer-Verlag, New York
    • 3. L. ALVAREZ, J. I. DIAZ, AND R. KERSNER, On the initial growth of the interfaces in nonlinear diffusion-convection processes, in "Nonlinear Diffusion Equations and Their Equilibrium States I" (W.-M. Ni, L. A. Peletier, and J. Serrin, Eds.), pp. 1-20, Springer-Verlag, New York, 1988.
    • (1988) Nonlinear Diffusion Equations and Their Equilibrium States , vol.1 , pp. 1-20
    • Alvarez, L.1    Diaz, J.I.2    Kersner, R.3
  • 6
    • 84972990576 scopus 로고
    • Local existence and uniqueness of solutions of degenerate parabolic equations
    • 6. J. R. ANDERSON, Local existence and uniqueness of solutions of degenerate parabolic equations, Comm. Partial Differential Equations 16 (1991), 105-143.
    • (1991) Comm. Partial Differential Equations , vol.16 , pp. 105-143
    • Anderson, J.R.1
  • 9
    • 0001483956 scopus 로고
    • Stabilization of solutions of a degenerate nonlinear diffusion problem
    • 9. D. ARONSON, M. G. CRANDALL, AND L. A. PELETIER, Stabilization of solutions of a degenerate nonlinear diffusion problem, Nonlinear Anal. 6 (1982), 1001-1022.
    • (1982) Nonlinear Anal. , vol.6 , pp. 1001-1022
    • Aronson, D.1    Crandall, M.G.2    Peletier, L.A.3
  • 10
    • 0002293879 scopus 로고
    • The porous medium equation
    • "Nonlinear Diffusion Problems" (A. Fasano and M. Primicerio, Eds.), Springer-Verlag, Berlin
    • 10. D. G. ARONSON, The porous medium equation, in "Nonlinear Diffusion Problems" (A. Fasano and M. Primicerio, Eds.), pp. 1-46, Lecture Notes in Mathematics, Vol. 1224, Springer-Verlag, Berlin, 1986.
    • (1986) Lecture Notes in Mathematics , vol.1224 , pp. 1-46
    • Aronson, D.G.1
  • 11
    • 84990602592 scopus 로고
    • Interfaces with a corner point in one-dimensional porous medium flow
    • 11. D. G. ARONSON, L. A. CAFFARELLI, AND J. L. VAZQUEZ, Interfaces with a corner point in one-dimensional porous medium flow, Comm. Pure Appl. Math. 38 (1985), 375-404.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 375-404
    • Aronson, D.G.1    Caffarelli, L.A.2    Vazquez, J.L.3
  • 12
    • 0002488752 scopus 로고
    • Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation
    • "Partial Differential Equations and Related Topics" (J. A. Goldstein, Ed.), Springer-Verlag, Berlin
    • 12. D. G. ARONSON AND H. F. WEINBERGER, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in "Partial Differential Equations and Related Topics" (J. A. Goldstein, Ed.), pp. 5-49, Lecture Notes in Mathematics, Vol.446, Springer-Verlag, Berlin, 1975.
    • (1975) Lecture Notes in Mathematics , vol.446 , pp. 5-49
    • Aronson, D.G.1    Weinberger, H.F.2
  • 13
    • 0003004337 scopus 로고
    • On some unsteady motions of a liquid and gas in a porous medium
    • 13. G. I. BARENBLATT, On some unsteady motions of a liquid and gas in a porous medium, Prikl. Mat. Mekh. 16 (1952), 67-78.
    • (1952) Prikl. Mat. Mekh. , vol.16 , pp. 67-78
    • Barenblatt, G.I.1
  • 14
    • 0011538415 scopus 로고
    • Self-similarity: Similarity and intermediate asymptotic form
    • 14. G. I. BLARENBLATT, Self-similarity: Similarity and intermediate asymptotic form, Radiophys. Quantum Electron. 19 (1976), 643-664. Translation of Izv. Vyssh. Uchebn. Zaved. Radiofiz. 19 (1976), 902-931.
    • (1976) Radiophys. Quantum Electron. , vol.19 , pp. 643-664
    • Blarenblatt, G.I.1
  • 15
    • 0011538415 scopus 로고
    • 14. G. I. BLARENBLATT, Self-similarity: Similarity and intermediate asymptotic form, Radiophys. Quantum Electron. 19 (1976), 643-664. Translation of Izv. Vyssh. Uchebn. Zaved. Radiofiz. 19 (1976), 902-931.
    • (1976) Izv. Vyssh. Uchebn. Zaved. Radiofiz. , vol.19 , pp. 902-931
  • 17
    • 0004072071 scopus 로고
    • Gordon and Breach Science Publishers, New York
    • 16. G. I. BARENBLATT, "Dimensional Analysis," Gordon and Breach Science Publishers, New York, 1987.
    • (1987) Dimensional Analysis
    • Barenblatt, G.I.1
  • 18
    • 84915503825 scopus 로고
    • Intermediate asymptotics in mathematical physics
    • 17. G. I. BARENBLATT AND YA. B. ZEL'DOVICH, Intermediate asymptotics in mathematical physics, Russ. Math. Surv. 26 (1971), 45-61. Translation of Uspekhi Mat. Nauk 26 (1971), 115-129.
    • (1971) Russ. Math. Surv. , vol.26 , pp. 45-61
    • Barenblatt, G.I.1    Zel'Dovich, Ya.B.2
  • 19
    • 84915503825 scopus 로고
    • 17. G. I. BARENBLATT AND YA. B. ZEL'DOVICH, Intermediate asymptotics in mathematical physics, Russ. Math. Surv. 26 (1971), 45-61. Translation of Uspekhi Mat. Nauk 26 (1971), 115-129.
    • (1971) Translation of Uspekhi Mat. Nauk , vol.26 , pp. 115-129
  • 20
    • 0000885949 scopus 로고
    • Self-similar solutions as intermediate asymptotics
    • 18. G. I. BARENBLATT AND YA. B. ZEL'DOVICH, Self-similar solutions as intermediate asymptotics, Annu. Rev. Fluid Mech. 4 (1972), 285-312.
    • (1972) Annu. Rev. Fluid Mech. , vol.4 , pp. 285-312
    • Barenblatt, G.I.1    Zel'Dovich, Ya.B.2
  • 24
    • 51249183721 scopus 로고
    • Comparison of solutions of nonlinear evolution problems with different nonlinear terms
    • 22. P. BÉNILAN AND J. I. DIAZ, Comparison of solutions of nonlinear evolution problems with different nonlinear terms, Israel J. Math. 42 (1982), 241-257.
    • (1982) Israel J. Math. , vol.42 , pp. 241-257
    • Bénilan, P.1    Diaz, J.I.2
  • 27
    • 0017768062 scopus 로고
    • Viscous sheets advancing over dry beds
    • 25. J. BUCKMASTER, Viscous sheets advancing over dry beds, J. Fluid Mech. 81 (1977), 735-756.
    • (1977) J. Fluid Mech. , vol.81 , pp. 735-756
    • Buckmaster, J.1
  • 30
    • 0001893870 scopus 로고
    • Application of a model system to illustrate some points of the statistical theory of free turbulence
    • 28. J. M. BURGERS, Application of a model system to illustrate some points of the statistical theory of free turbulence, Proc. Kon. Nederl. Akad. Wetensch. 43 (1940), 2-12.
    • (1940) Proc. Kon. Nederl. Akad. Wetensch. , vol.43 , pp. 2-12
    • Burgers, J.M.1
  • 31
    • 77956834067 scopus 로고
    • A mathematical model illustrating the theory of turbulence
    • 29. J. M. BURGERS, A mathematical model illustrating the theory of turbulence, Adv. Appl. Mech. 1 (1948), 171-199.
    • (1948) Adv. Appl. Mech. , vol.1 , pp. 171-199
    • Burgers, J.M.1
  • 33
    • 0011599553 scopus 로고
    • The propagation of nonstationary filtration with absorption
    • 31. C. CHEN, The propagation of nonstationary filtration with absorption, Acta. Math. Appl. Sinica (English Ser.) 3 (1987), 342-350.
    • (1987) Acta. Math. Appl. Sinica (English Ser.) , vol.3 , pp. 342-350
    • Chen, C.1
  • 34
    • 0002833991 scopus 로고
    • Finite-point extinction and continuity of interfaces in a nonlinear diffusion equation with strong absorption
    • 32. X.-Y. CHEN, H. MATANO, AND M. MIMURA, Finite-point extinction and continuity of interfaces in a nonlinear diffusion equation with strong absorption, J. Reine Angew. Math. 459 (1995), 1-36.
    • (1995) J. Reine Angew. Math. , vol.459 , pp. 1-36
    • Chen, X.-Y.1    Matano, H.2    Mimura, M.3
  • 36
    • 0000023029 scopus 로고
    • Asymptotic behavior of the solutions of a nonlinear Fokker-Planck equation with Dirichlet boundary conditions
    • 34. E. COMPARINI, R. RICCI, AND J. L. VAZQUEZ, Asymptotic behavior of the solutions of a nonlinear Fokker-Planck equation with Dirichlet boundary conditions, J. Math. Anal. Appl. 175 (1993), 606-631.
    • (1993) J. Math. Anal. Appl. , vol.175 , pp. 606-631
    • Comparini, E.1    Ricci, R.2    Vazquez, J.L.3
  • 37
    • 0016820684 scopus 로고
    • A method for measuring the spatial distribution of tissue oxygen removal rates
    • 35. T. B. CONSTABLE AND N. T. S. EVANS, A method for measuring the spatial distribution of tissue oxygen removal rates, Respir. Physiol. 25 (1975), 175-190.
    • (1975) Respir. Physiol. , vol.25 , pp. 175-190
    • Constable, T.B.1    Evans, N.T.S.2
  • 38
    • 38249024429 scopus 로고
    • Localization and boundedness of the solutions of the Neumann problem for a filtration equation
    • 36. C. CORTAZAR AND M. ELGUETA, Localization and boundedness of the solutions of the Neumann problem for a filtration equation, Nonlinear Anal. 13 (1989), 33-41.
    • (1989) Nonlinear Anal. , vol.13 , pp. 33-41
    • Cortazar, C.1    Elgueta, M.2
  • 41
    • 77958399004 scopus 로고
    • A moving boundary problem arising from the diffusion of oxygen in absorbing tissue
    • 39. J. CRANK AND R. S. GUPTA, A moving boundary problem arising from the diffusion of oxygen in absorbing tissue, J. Inst. Math. Appl. 10 (1972), 19-33.
    • (1972) J. Inst. Math. Appl. , vol.10 , pp. 19-33
    • Crank, J.1    Gupta, R.S.2
  • 42
    • 0011599554 scopus 로고
    • Non existence d'une des frontières libres dans une équation dégénérée en théorie de la filtration
    • 40. J. I. DIAZ AND R. KERSNER, Non existence d'une des frontières libres dans une équation dégénérée en théorie de la filtration, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), 505-508.
    • (1983) C. R. Acad. Sci. Paris Sér. I Math. , vol.296 , pp. 505-508
    • Diaz, J.I.1    Kersner, R.2
  • 43
    • 38249034235 scopus 로고
    • On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium
    • 41. J. I. DIAZ AND R. KERSNER, On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium, J. Differential Equations 69 (1987), 368-403.
    • (1987) J. Differential Equations , vol.69 , pp. 368-403
    • Diaz, J.I.1    Kersner, R.2
  • 44
    • 38249028399 scopus 로고
    • On the behaviour and cases of nonexistence of the free boundary in a semibounded porous medium
    • 42. J. I. DIAZ AND R. KERSNER, On the behaviour and cases of nonexistence of the free boundary in a semibounded porous medium, J. Math. Anal. Appl. 132 (1988), 281-289.
    • (1988) J. Math. Anal. Appl. , vol.132 , pp. 281-289
    • Diaz, J.I.1    Kersner, R.2
  • 45
    • 0000132534 scopus 로고
    • Implicit degenerate evolution equations and applications
    • 43. E. DI BENEDETTO AND R. E. SHOWALTER, Implicit degenerate evolution equations and applications, SIAM J. Math. Anal. 12 (1981), 731-751.
    • (1981) SIAM J. Math. Anal. , vol.12 , pp. 731-751
    • Di Benedetto, E.1    Showalter, R.E.2
  • 47
    • 85040804842 scopus 로고
    • Cambridge Univ. Press, Cambridge, U.K.
    • 45. P. G. DRAZIN, "Solitons," Cambridge Univ. Press, Cambridge, U.K., 1983.
    • (1983) Solitons
    • Drazin, P.G.1
  • 49
    • 38249020188 scopus 로고
    • Large time behaviour of solutions of the porous medium equation with convection
    • 47. C. J. VAN DUIJN AND J. M. DE GRAAF, Large time behaviour of solutions of the porous medium equation with convection, J. Differential Equations 84 (1990), 183-203.
    • (1990) J. Differential Equations , vol.84 , pp. 183-203
    • Van Duijn, C.J.1    De Graaf, J.M.2
  • 50
    • 0011603510 scopus 로고
    • Solute transport through porous media with slow adsorption
    • (K. H. Hoffmann and J. Sprekels, Eds.), Longman, Harlow, U.K.
    • 48. C. J. VAN DUIJN AND P. KNABNER, Solute transport through porous media with slow adsorption, in "Free Boundary Problems: Theory and Applications, Vol. I" (K. H. Hoffmann and J. Sprekels, Eds.), pp. 375-388, Longman, Harlow, U.K., 1990.
    • (1990) Free Boundary Problems: Theory and Applications , vol.1 , pp. 375-388
    • Van Duijn, C.J.1    Knabner, P.2
  • 51
    • 0001529380 scopus 로고
    • Résolution d'un problème de stefan (fusion d'un bloc de glace à zéro degré)
    • 49. G. DUVAUT, Résolution d'un problème de Stefan (Fusion d'un bloc de glace à zéro degré), C. R. Acad. Sci. Paris Sér. A 276 (1973), 1461-1463.
    • (1973) C. R. Acad. Sci. Paris Sér. A , vol.276 , pp. 1461-1463
    • Duvaut, G.1
  • 53
    • 84972539551 scopus 로고
    • Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities
    • 51. L. C. EVANS AND B. F. KNERR, Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities, Illinois J. Math. 23 (1979), 153-166.
    • (1979) Illinois J. Math. , vol.23 , pp. 153-166
    • Evans, L.C.1    Knerr, B.F.2
  • 54
    • 84966218113 scopus 로고
    • Asymptotic states for equations of reaction and diffusion
    • 52. P. C. FIFE, Asymptotic states for equations of reaction and diffusion, Bull. Amer. Math. Soc. (N. S.) 84 (1978), 693-726.
    • (1978) Bull. Amer. Math. Soc. (N. S.) , vol.84 , pp. 693-726
    • Fife, P.C.1
  • 56
    • 84968501796 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to travelling wave solutions
    • 54. P. C. FIFE AND J. B. MCLEOD, The approach of solutions of nonlinear diffusion equations to travelling wave solutions, Bull. Amer. Math. Soc. (N. S.) 81 (1975), 1076-1078.
    • (1975) Bull. Amer. Math. Soc. (N. S.) , vol.81 , pp. 1076-1078
    • Fife, P.C.1    McLeod, J.B.2
  • 57
    • 0017637590 scopus 로고
    • The approach of solutions of nonlinear diffusion equations to travelling front solutions
    • 55. P. C. FIFE AND J. B. MCLEOD, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Rational Mech. Anal. 65 (1977), 335-361.
    • (1977) Arch. Rational Mech. Anal. , vol.65 , pp. 335-361
    • Fife, P.C.1    McLeod, J.B.2
  • 58
    • 0000268135 scopus 로고
    • The wave of advance of advantageous genes
    • 56. R. A. FISHER, The wave of advance of advantageous genes, Ann. Eugen. 7 (1937), 355-369.
    • (1937) Ann. Eugen. , vol.7 , pp. 355-369
    • Fisher, R.A.1
  • 59
    • 0011669865 scopus 로고
    • On the porous medium equations with lower order singular nonlinear terms
    • 57. G. FRANCSICS, On the porous medium equations with lower order singular nonlinear terms, Acta Math. Hungar. 45 (1985), 425-436.
    • (1985) Acta Math. Hungar. , vol.45 , pp. 425-436
    • Francsics, G.1
  • 62
    • 0011541421 scopus 로고
    • Some properties of travelling waves in a medium with non-linear thermal conductivity and a source of heat
    • 60. V. A. GALAKTIONOV, Some properties of travelling waves in a medium with non-linear thermal conductivity and a source of heat, U.S.S.R. Comput. Math. Math. Phys. 21 (1981), 167-176. Translation of Zh. Vychisl. Mat. Mat. Fiz. 21 (1981), 980-989.
    • (1981) U.S.S.R. Comput. Math. Math. Phys. , vol.21 , pp. 167-176
    • Galaktionov, V.A.1
  • 63
    • 0011541421 scopus 로고
    • 60. V. A. GALAKTIONOV, Some properties of travelling waves in a medium with non-linear thermal conductivity and a source of heat, U.S.S.R. Comput. Math. Math. Phys. 21 (1981), 167-176. Translation of Zh. Vychisl. Mat. Mat. Fiz. 21 (1981), 980-989.
    • (1981) Zh. Vychisl. Mat. Mat. Fiz. , vol.21 , pp. 980-989
  • 65
    • 0011600922 scopus 로고
    • x + uβ, Differential Equations 21 (1985), 11-18. Translation of Differentsial'nye Urav. 21 (1985), 15-23.
    • (1985) Differentsial'nye Urav. , vol.21 , pp. 15-23
  • 67
    • 0011669866 scopus 로고
    • σ+1, Differential Equations 21 (1986), 751-758. Translation of Differentsial'nye Urav. 21 (1985), 1126-1134.
    • (1985) Differentsial'nye Urav. , vol.21 , pp. 1126-1134
  • 68
    • 0011594434 scopus 로고
    • x + uβ near a "singular" point
    • x + uβ near a "singular" point, Soviet Math. Dokl. 33 (1986), 840-844. Translation of Dokl. Akad. Nauk SSSR 288 (1986), 1293-1297.
    • (1986) Soviet Math. Dokl. , vol.33 , pp. 840-844
    • Galaktionov, V.A.1
  • 69
    • 0011540275 scopus 로고
    • x + uβ near a "singular" point, Soviet Math. Dokl. 33 (1986), 840-844. Translation of Dokl. Akad. Nauk SSSR 288 (1986), 1293-1297.
    • (1986) Dokl. Akad. Nauk SSSR , vol.288 , pp. 1293-1297
  • 70
    • 0011541422 scopus 로고
    • Accurate estimates for the amplitude and support of unbounded solutions of the non-linear heat-conduction equation with a source
    • 64. V. A. GALAKTIONOV, Accurate estimates for the amplitude and support of unbounded solutions of the non-linear heat-conduction equation with a source, U.S.S.R. Comput. Math. Math. Phys. 30 (1990), 67-74. Translation of Zh. Vychisl. Mat. Mat. Fiz. 30 (1990), 438-448.
    • (1990) U.S.S.R. Comput. Math. Math. Phys. , vol.30 , pp. 67-74
    • Galaktionov, V.A.1
  • 71
    • 0011541422 scopus 로고
    • 64. V. A. GALAKTIONOV, Accurate estimates for the amplitude and support of unbounded solutions of the non-linear heat-conduction equation with a source, U.S.S.R. Comput. Math. Math. Phys. 30 (1990), 67-74. Translation of Zh. Vychisl. Mat. Mat. Fiz. 30 (1990), 438-448.
    • (1990) Zh. Vychisl. Mat. Mat. Fiz. , vol.30 , pp. 438-448
  • 72
    • 0000036454 scopus 로고
    • A quasilinear heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures
    • 65. V. A. GALAKTIONOV, V. A. DORODNITSYN, G. G. ELENIN, S. P. KURDYUMOV, AND A. A. SAMARSKII, A quasilinear heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures, J. Soviet Math. 41 (1988), 1222-1292. Translation of Itog. Nauk. Tekhn. 28 (1986), 95-206.
    • (1988) J. Soviet Math. , vol.41 , pp. 1222-1292
    • Galaktionov, V.A.1    Dorodnitsyn, V.A.2    Elenin, G.G.3    Kurdyumov, S.P.4    Samarskii, A.A.5
  • 73
    • 0000036454 scopus 로고
    • 65. V. A. GALAKTIONOV, V. A. DORODNITSYN, G. G. ELENIN, S. P. KURDYUMOV, AND A. A. SAMARSKII, A quasilinear heat equation with a source: Peaking, localization, symmetry exact solutions, asymptotics, structures, J. Soviet Math. 41 (1988), 1222-1292. Translation of Itog. Nauk. Tekhn. 28 (1986), 95-206.
    • (1986) Itog. Nauk. Tekhn. , vol.28 , pp. 95-206
  • 74
    • 0011651917 scopus 로고
    • Monotonicity of a solution of a degenerate quasilinear parabolic equation
    • 66. V. A. GALAKTIONOV AND S. A. POSASHKOV, Monotonicity of a solution of a degenerate quasilinear parabolic equation, Differential Equations 26 (1991), 819-827. Translation of Differentsial'nye Urav. 26 (1990), 1127-1136.
    • (1991) Differential Equations , vol.26 , pp. 819-827
    • Galaktionov, V.A.1    Posashkov, S.A.2
  • 75
    • 0011603089 scopus 로고
    • 66. V. A. GALAKTIONOV AND S. A. POSASHKOV, Monotonicity of a solution of a degenerate quasilinear parabolic equation, Differential Equations 26 (1991), 819-827. Translation of Differentsial'nye Urav. 26 (1990), 1127-1136.
    • (1990) Differentsial'nye Urav. , vol.26 , pp. 1127-1136
  • 77
    • 0017728713 scopus 로고
    • Properties of solutions of an equation in the theory of infiltration
    • 68. B. H. GILDING, Properties of solutions of an equation in the theory of infiltration, Arch. Rational Mech. Anal. 65 (1977), 203-225.
    • (1977) Arch. Rational Mech. Anal. , vol.65 , pp. 203-225
    • Gilding, B.H.1
  • 78
    • 0001662607 scopus 로고
    • A nonlinear degenerate parabolic equation
    • 69. B. H. GILDING, A nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), 393-432.
    • (1977) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.4 , Issue.4 , pp. 393-432
    • Gilding, B.H.1
  • 79
    • 0000287076 scopus 로고
    • Stabilization of flows through porous media
    • 70. B. H. GILDING, Stabilization of flows through porous media, SIAM J. Math. Anal. 10 (1979), 237-246.
    • (1979) SIAM J. Math. Anal. , vol.10 , pp. 237-246
    • Gilding, B.H.1
  • 80
    • 0002483505 scopus 로고
    • The occurrence of interfaces in nonlinear diffusion-advection processes
    • 71. B. H. GILDING, The occurrence of interfaces in nonlinear diffusion-advection processes, Arch. Rational Mech. Anal. 100 (1988), 243-263.
    • (1988) Arch. Rational Mech. Anal. , vol.100 , pp. 243-263
    • Gilding, B.H.1
  • 81
    • 0001279719 scopus 로고
    • Improved theory for a nonlinear degenerate parabolic equation
    • 72. B. H. GILDING, Improved theory for a nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), 165-224; 17 (1990), 479.
    • (1989) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.16 , Issue.4 , pp. 165-224
    • Gilding, B.H.1
  • 82
    • 0009181934 scopus 로고
    • 72. B. H. GILDING, Improved theory for a nonlinear degenerate parabolic equation, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16 (1989), 165-224; 17 (1990), 479.
    • (1990) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.17 , pp. 479
  • 83
    • 38249005296 scopus 로고
    • Localization of solutions of a nonlinear Fokker-Planck equation with Dirichlet boundary conditions
    • 73. B. H. GILDING, Localization of solutions of a nonlinear Fokker-Planck equation with Dirichlet boundary conditions, Nonlinear Anal. 13 (1989), 1215-1240.
    • (1989) Nonlinear Anal. , vol.13 , pp. 1215-1240
    • Gilding, B.H.1
  • 84
    • 0026241143 scopus 로고
    • Qualitative mathematical analysis of the Richards equation
    • 74. B. H. GILDING, Qualitative mathematical analysis of the Richards equation, Transport Porous Med. 5 (1991), 651-666.
    • (1991) Transport Porous Med. , vol.5 , pp. 651-666
    • Gilding, B.H.1
  • 85
    • 0011601698 scopus 로고
    • A singular nonlinear Volterra integral equation
    • 75. B. H. GILDING, A singular nonlinear Volterra integral equation, J. Integral Equations Appl. 5 (1993), 465-502.
    • (1993) J. Integral Equations Appl. , vol.5 , pp. 465-502
    • Gilding, B.H.1
  • 86
    • 84966220953 scopus 로고
    • Instantaneous shrinking in nonlinear diffusion-convection
    • 76. B. H. GILDING AND R. KERSNER, Instantaneous shrinking in nonlinear diffusion-convection, Proc. Amer. Math. Soc. 109 (1990), 385-394.
    • (1990) Proc. Amer. Math. Soc. , vol.109 , pp. 385-394
    • Gilding, B.H.1    Kersner, R.2
  • 87
    • 0011605814 scopus 로고
    • Diffusion-convection-réaction, frontières libres et une équation intégrale
    • 77. B. H. GILDING AND R. KERSNER, Diffusion-convection-réaction, frontières libres et une équation intégrale, C. R. Acad. Sci. Paris Sér. I Math. 313 (1991), 743-746.
    • (1991) C. R. Acad. Sci. Paris Sér. I Math. , vol.313 , pp. 743-746
    • Gilding, B.H.1    Kersner, R.2
  • 89
    • 0000943090 scopus 로고
    • Asymptotic solution of a model non-linear convective diffusion equation
    • 79. R. E. GRUNDY, Asymptotic solution of a model non-linear convective diffusion equation, IMA J. Appl. Math. 31 (1983), 121-137.
    • (1983) IMA J. Appl. Math. , vol.31 , pp. 121-137
    • Grundy, R.E.1
  • 90
    • 0011599565 scopus 로고
    • The Cauchy problem for a nonlinear diffusion equation with absorption and convection
    • 80. R. E. GRUNDY, The Cauchy problem for a nonlinear diffusion equation with absorption and convection, IMA J. Appl. Math. 40 (1988), 183-204.
    • (1988) IMA J. Appl. Math. , vol.40 , pp. 183-204
    • Grundy, R.E.1
  • 91
    • 84976003977 scopus 로고
    • Short time behaviour of a singular solution to the heat equation with absorption
    • 81. R. E. GRUNDY AND L. A. PELETIER, Short time behaviour of a singular solution to the heat equation with absorption, Proc. Roy. Soc. Edinburgh Sect. A 107 (1987), 271-288.
    • (1987) Proc. Roy. Soc. Edinburgh Sect. A , vol.107 , pp. 271-288
    • Grundy, R.E.1    Peletier, L.A.2
  • 92
    • 38249015378 scopus 로고
    • The one-dimensional porous medium equation with convection: Continuous differentiability of interfaces after the waiting time
    • 82. M. GUEDDA, D. HILHORST, AND C. PICARD, The one-dimensional porous medium equation with convection: Continuous differentiability of interfaces after the waiting time, Appl. Math. Lett. 5 (1992), 59-62.
    • (1992) Appl. Math. Lett. , vol.5 , pp. 59-62
    • Guedda, M.1    Hilhorst, D.2    Picard, C.3
  • 93
    • 0016753474 scopus 로고
    • The regulation of inhomogeneous populations
    • 83. W. S. C. GURNEY AND R. M. NISBET, The regulation of inhomogeneous populations, J. Theoret. Biol. 52 (1975), 441-457.
    • (1975) J. Theoret. Biol. , vol.52 , pp. 441-457
    • Gurney, W.S.C.1    Nisbet, R.M.2
  • 94
    • 0017357730 scopus 로고
    • On the diffusion of biological populations
    • 84. M. E. GURTIN AND R. C. MACCAMY, On the diffusion of biological populations, Math. Biosci. 33 (1977), 35-49.
    • (1977) Math. Biosci. , vol.33 , pp. 35-49
    • Gurtin, M.E.1    MacCamy, R.C.2
  • 95
    • 0001166785 scopus 로고
    • The one-dimensional nonlinear heat equation with absorption: Regularity of solutions and interfaces
    • 85. M. A. HERRERO AND J. L. VÁZQUEZ, The one-dimensional nonlinear heat equation with absorption: Regularity of solutions and interfaces, SIAM J. Math. Anal. 18 (1987), 149-167.
    • (1987) SIAM J. Math. Anal. , vol.18 , pp. 149-167
    • Herrero, M.A.1    Vázquez, J.L.2
  • 97
    • 0011541032 scopus 로고
    • C∞-regularity for the porous medium equation
    • 87. K. HÖLLIG AND H.-O. KREISS, C∞-regularity for the porous medium equation, Math. Z. 192 (1986), 217-224.
    • (1986) Math. Z. , vol.192 , pp. 217-224
    • Höllig, K.1    Kreiss, H.-O.2
  • 98
    • 0000538051 scopus 로고
    • The occurrence of singularities in solutions of the non-steady see-page equation
    • 88. A. S. KALASHNIKOV, The occurrence of singularities in solutions of the non-steady see-page equation, U.S.S.R. Comput. Math. Math. Phys. 7 (1967), 269-275. Translation of Zh. Vychisl. Mat. Mat. Fiz. 7 (1967), 440-444.
    • (1967) U.S.S.R. Comput. Math. Math. Phys. , vol.7 , pp. 269-275
    • Kalashnikov, A.S.1
  • 99
    • 0000538051 scopus 로고
    • 88. A. S. KALASHNIKOV, The occurrence of singularities in solutions of the non-steady see-page equation, U.S.S.R. Comput. Math. Math. Phys. 7 (1967), 269-275. Translation of Zh. Vychisl. Mat. Mat. Fiz. 7 (1967), 440-444.
    • (1967) Zh. Vychisl. Mat. Mat. Fiz. , vol.7 , pp. 440-444
  • 100
    • 0011541859 scopus 로고
    • On equations of the nonstationary-filtration type in which the perturbation is propagated at infinite velocity
    • 89. A. S. KALASHNIKOV, On equations of the nonstationary-filtration type in which the perturbation is propagated at infinite velocity, Moscow Univ. Math. Bull. 27 (1972), 104-108. Translation of Vestn. Moskov. Univ. Ser. I Mat. Mekh. 27 (1972), 45-49.
    • (1972) Moscow Univ. Math. Bull. , vol.27 , pp. 104-108
    • Kalashnikov, A.S.1
  • 101
    • 0011538423 scopus 로고
    • 89. A. S. KALASHNIKOV, On equations of the nonstationary-filtration type in which the perturbation is propagated at infinite velocity, Moscow Univ. Math. Bull. 27 (1972), 104-108. Translation of Vestn. Moskov. Univ. Ser. I Mat. Mekh. 27 (1972), 45-49.
    • (1972) Vestn. Moskov. Univ. Ser. I Mat. Mekh. , vol.27 , pp. 45-49
  • 102
    • 0002168217 scopus 로고
    • On the differential properties of generalized solutions of equations of the nonsteady-state filtration type
    • 90. A. S. KALASHNIKOV, On the differential properties of generalized solutions of equations of the nonsteady-state filtration type, Moscow Univ. Math. Bull. 29 (1974), 48-53. Translation of Vestn. Moskov. Univ. Ser. I Mat. Mekh. 29 (1974), 62-68.
    • (1974) Moscow Univ. Math. Bull. , vol.29 , pp. 48-53
    • Kalashnikov, A.S.1
  • 103
    • 0003192426 scopus 로고
    • 90. A. S. KALASHNIKOV, On the differential properties of generalized solutions of equations of the nonsteady-state filtration type, Moscow Univ. Math. Bull. 29 (1974), 48-53. Translation of Vestn. Moskov. Univ. Ser. I Mat. Mekh. 29 (1974), 62-68.
    • (1974) Vestn. Moskov. Univ. Ser. I Mat. Mekh. , vol.29 , pp. 62-68
  • 104
    • 0000441642 scopus 로고
    • The propagation of disturbances in problems of non-linear heat conduction with absorption
    • 91. A. S. KALASHNIKOV, The propagation of disturbances in problems of non-linear heat conduction with absorption, U.S.S.R. Comput. Math. Math. Phys. 14 (1974), 70-85. Translation of Zh. Vychisl. Mat. Mat. Fiz. 14 (1974), 891-905.
    • (1974) U.S.S.R. Comput. Math. Math. Phys. , vol.14 , pp. 70-85
    • Kalashnikov, A.S.1
  • 105
    • 0000441642 scopus 로고
    • 91. A. S. KALASHNIKOV, The propagation of disturbances in problems of non-linear heat conduction with absorption, U.S.S.R. Comput. Math. Math. Phys. 14 (1974), 70-85. Translation of Zh. Vychisl. Mat. Mat. Fiz. 14 (1974), 891-905.
    • (1974) Zh. Vychisl. Mat. Mat. Fiz. , vol.14 , pp. 891-905
  • 106
    • 0011605815 scopus 로고
    • The nature of the propagation of perturbations in processes that can be described by quasilinear degenerate parabolic equations
    • In Russian
    • 92. A. S. KALASHNIKOV, The nature of the propagation of perturbations in processes that can be described by quasilinear degenerate parabolic equations, Trud. Sem. Petrovsk. 1 (1975), 135-144. [In Russian]
    • (1975) Trud. Sem. Petrovsk. , vol.1 , pp. 135-144
    • Kalashnikov, A.S.1
  • 107
    • 0011599566 scopus 로고
    • The effect of absorption on heat propagation in a medium in which the thermal conductivity depends on temperature
    • 93. A. S. KALASHNIKOV, The effect of absorption on heat propagation in a medium in which the thermal conductivity depends on temperature, U.S.S.R. Comput. Math. Math. Phys. 16 (1976), 141-149. Translation of Zh. Vychisl. Mat. Mat. Fiz. 16 (1976), 689-696.
    • (1976) U.S.S.R. Comput. Math. Math. Phys. , vol.16 , pp. 141-149
    • Kalashnikov, A.S.1
  • 108
    • 0011599566 scopus 로고
    • 93. A. S. KALASHNIKOV, The effect of absorption on heat propagation in a medium in which the thermal conductivity depends on temperature, U.S.S.R. Comput. Math. Math. Phys. 16 (1976), 141-149. Translation of Zh. Vychisl. Mat. Mat. Fiz. 16 (1976), 689-696.
    • (1976) Zh. Vychisl. Mat. Mat. Fiz. , vol.16 , pp. 689-696
  • 109
    • 84862599035 scopus 로고
    • Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations
    • 94. A. S. KALASHNIKOV, Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations, Russ. Math. Surveys 42 (1987), 169-222. Translation of Uspekhi Mat. Nauk 42 (1987), 135-176.
    • (1987) Russ. Math. Surveys , vol.42 , pp. 169-222
    • Kalashnikov, A.S.1
  • 110
    • 84862599035 scopus 로고
    • 94. A. S. KALASHNIKOV, Some problems of the qualitative theory of non-linear degenerate second-order parabolic equations, Russ. Math. Surveys 42 (1987), 169-222. Translation of Uspekhi Mat. Nauk 42 (1987), 135-176.
    • (1987) Uspekhi Mat. Nauk , vol.42 , pp. 135-176
  • 111
    • 51249188354 scopus 로고
    • The asumptotic behaviour of the solution of the filtration equation
    • 95. S. KAMENOMOSTSKAYA, The asumptotic behaviour of the solution of the filtration equation, Israel J. Math. 14 (1973), 76-87.
    • (1973) Israel J. Math. , vol.14 , pp. 76-87
    • Kamenomostskaya, S.1
  • 112
    • 0016900774 scopus 로고
    • Similar solutions and the asymptotics of filtration equations
    • 96. S. KAMIN (KAMENOMOSTSKAYA), Similar solutions and the asymptotics of filtration equations, Arch. Rational Mech. Anal. 60 (1976), 171-183.
    • (1976) Arch. Rational Mech. Anal. , vol.60 , pp. 171-183
    • Kamenomostskaya, S.K.1
  • 113
    • 0011600923 scopus 로고
    • Localization conditions for thermal perturbations in a semibounded moving medium with absorption
    • 97. R. KERSHNER, Localization conditions for thermal perturbations in a semibounded moving medium with absorption, Moscow Univ. Math. Bull 31 (1976), 90-95. Translation of Vestn. Moskov. Univ. Ser. I Mat. Mekh. 31 (1976), 52-58.
    • (1976) Moscow Univ. Math. Bull , vol.31 , pp. 90-95
    • Kershner, R.1
  • 114
    • 0011538424 scopus 로고
    • 97. R. KERSHNER, Localization conditions for thermal perturbations in a semibounded moving medium with absorption, Moscow Univ. Math. Bull 31 (1976), 90-95. Translation of Vestn. Moskov. Univ. Ser. I Mat. Mekh. 31 (1976), 52-58.
    • (1976) Vestn. Moskov. Univ. Ser. I Mat. Mekh. , vol.31 , pp. 52-58
  • 115
    • 0000632472 scopus 로고
    • Some properties of generalized solutions of quasilinear parabolic equations
    • In Russian
    • 98. R. KERSHNER, Some properties of generalized solutions of quasilinear parabolic equations, Acta Math. Acad. Sci. Hungar. 32 (1978), 301-330. [In Russian]
    • (1978) Acta Math. Acad. Sci. Hungar. , vol.32 , pp. 301-330
    • Kershner, R.1
  • 116
    • 0000482998 scopus 로고
    • The behavior of the solutions of degenerate quasilinear parabolic equation as t → ∞
    • In Russian
    • 99. R. KERSHNER, The behavior of the solutions of degenerate quasilinear parabolic equation as t → ∞, Acta Math. Acad. Sci. Hungar. 34 (1979), 157-163. [In Russian]
    • (1979) Acta Math. Acad. Sci. Hungar. , vol.34 , pp. 157-163
    • Kershner, R.1
  • 117
    • 0011601699 scopus 로고
    • The behavior of temperature fronts in media with nonlinear thermal conductivity under absorption
    • 100. R. KERSNER, The behavior of temperature fronts in media with nonlinear thermal conductivity under absorption, Moscow Univ. Math. Bull. 33 (1978), 35-41. Translation of Vestn. Moskov. Univ. Ser. I Mat. Mekh. 33 (1978), 44-51.
    • (1978) Moscow Univ. Math. Bull. , vol.33 , pp. 35-41
    • Kersner, R.1
  • 118
    • 0011601353 scopus 로고
    • 100. R. KERSNER, The behavior of temperature fronts in media with nonlinear thermal conductivity under absorption, Moscow Univ. Math. Bull. 33 (1978), 35-41. Translation of Vestn. Moskov. Univ. Ser. I Mat. Mekh. 33 (1978), 44-51.
    • (1978) Vestn. Moskov. Univ. Ser. I Mat. Mekh. , vol.33 , pp. 44-51
  • 119
    • 84990263481 scopus 로고
    • Degenerate parabolic equations with general nonlinearities
    • 101. R. KERSNER, Degenerate parabolic equations with general nonlinearities, Nonlinear Anal. 4 (1980), 1043-1062.
    • (1980) Nonlinear Anal. , vol.4 , pp. 1043-1062
    • Kersner, R.1
  • 120
    • 0011657181 scopus 로고
    • Filtration with absorption: Necessary and sufficient condition for the propagation of perturbations to have finite velocity
    • 102. R. KERSNER, Filtration with absorption: Necessary and sufficient condition for the propagation of perturbations to have finite velocity, J. Math. Anal. Appl. 90 (1982), 463-479.
    • (1982) J. Math. Anal. Appl. , vol.90 , pp. 463-479
    • Kersner, R.1
  • 121
    • 0020880558 scopus 로고
    • Nonlinear heat conduction with absorption: Space localization and extinction in finite time
    • 103. R. KERSNER, Nonlinear heat conduction with absorption: Space localization and extinction in finite time, SIAM J. Appl. Math. 43 (1983), 1274-1285.
    • (1983) SIAM J. Appl. Math. , vol.43 , pp. 1274-1285
    • Kersner, R.1
  • 122
    • 0011596110 scopus 로고
    • The limiting moisture profile during infiltration in to a homogeneous soil
    • 104. N. V. KHUSNYTDINOVA, The limiting moisture profile during infiltration in to a homogeneous soil, J. Appl. Math. Mech. 31 (1967), 783-789. Translation of Prikl. Mat. Mekh. 31 (1967), 770-776.
    • (1967) J. Appl. Math. Mech. , vol.31 , pp. 783-789
    • Khusnytdinova, N.V.1
  • 123
    • 0011596110 scopus 로고
    • 104. N. V. KHUSNYTDINOVA, The limiting moisture profile during infiltration in to a homogeneous soil, J. Appl. Math. Mech. 31 (1967), 783-789. Translation of Prikl. Mat. Mekh. 31 (1967), 770-776.
    • (1967) Prikl. Mat. Mekh. , vol.31 , pp. 770-776
  • 124
    • 0002722044 scopus 로고
    • Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application a un problème biologique
    • 105. A. KOLMOGOROFF, I. PETROVSKY, AND N. PISCOUNOFF, Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application a un problème biologique, Bull. Univ. Moscou Sér. Internat. Sect. A Math. Méc. 1 (1937), 1-25.
    • (1937) Bull. Univ. Moscou Sér. Internat. Sect. A Math. Méc. , vol.1 , pp. 1-25
    • Kolmogoroff, A.1    Petrovsky, I.2    Piscounoff, N.3
  • 125
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
    • 106. D. J. KORTEWEG AND G. DE VRIES, On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Phil. Mag. 39 (1895), 422-443.
    • (1895) Phil. Mag. , vol.39 , pp. 422-443
    • Korteweg, D.J.1    De Vries, G.2
  • 127
    • 0011604882 scopus 로고
    • The problem of the three-dimensional localization of thermal perturbations in the theory of non-linear heat conduction
    • 108. L. K. MARTINSON AND K. B. PAVLOV, The problem of the three-dimensional localization of thermal perturbations in the theory of non-linear heat conduction, U.S.S.R. Comput. Math. Math. Phys 12 (1972), 261-268. Translation of Zh. Vychisl. Mat. Mat. Fiz. 12 (1972), 1048-1053.
    • (1972) U.S.S.R. Comput. Math. Math. Phys , vol.12 , pp. 261-268
    • Martinson, L.K.1    Pavlov, K.B.2
  • 128
    • 0011604882 scopus 로고
    • 108. L. K. MARTINSON AND K. B. PAVLOV, The problem of the three-dimensional localization of thermal perturbations in the theory of non-linear heat conduction, U.S.S.R. Comput. Math. Math. Phys 12 (1972), 261-268. Translation of Zh. Vychisl. Mat. Mat. Fiz. 12 (1972), 1048-1053.
    • (1972) Zh. Vychisl. Mat. Mat. Fiz. , vol.12 , pp. 1048-1053
  • 130
    • 0000644794 scopus 로고
    • Spatial contact models for ecological and epidemic spread
    • 110. D. MOLLISON, Spatial contact models for ecological and epidemic spread, J. Roy. Statist. Soc. Ser. B 39 (1977), 283-326.
    • (1977) J. Roy. Statist. Soc. Ser. B , vol.39 , pp. 283-326
    • Mollison, D.1
  • 135
    • 0001217997 scopus 로고
    • The Cauchy problem and boundary problems for equations of the type of non-stationary filtration
    • In Russian
    • 115. O. A. OLEINIK, A. S. KALASHNIKOV, AND CHZHOU Y.-L., The Cauchy problem and boundary problems for equations of the type of non-stationary filtration, Izv. Akad. Nauk SSSR Ser. Mat. 22 (1958), 667-704. [In Russian]
    • (1958) Izv. Akad. Nauk SSSR Ser. Mat. , vol.22 , pp. 667-704
    • Oleinik, O.A.1    Kalashnikov, A.S.2    Chzhou, Y.-L.3
  • 136
    • 0001609271 scopus 로고
    • Quasi-linear second-order parabolic equations with many independent variables
    • 116. O. A. OLEINIK AND S. N. KRUZHKOV, Quasi-linear second-order parabolic equations with many independent variables, Russ. Math. Surv. 16 (1961), 105-146.
    • (1961) Russ. Math. Surv. , vol.16 , pp. 105-146
    • Oleinik, O.A.1    Kruzhkov, S.N.2
  • 137
    • 0001609275 scopus 로고
    • Translation of Uspekhi Mat. Nauk 16 (1961), 115-155.
    • (1961) Uspekhi Mat. Nauk , vol.16 , pp. 115-155
  • 138
  • 139
    • 0002849414 scopus 로고
    • Travelling waves and finite propagation in a reaction-diffusion equation
    • 118. A. DE PABLO AND J. L. VAZQUEZ, Travelling waves and finite propagation in a reaction-diffusion equation, J. Differential Equations 93 (1991), 19-61.
    • (1991) J. Differential Equations , vol.93 , pp. 19-61
    • De Pablo, A.1    Vazquez, J.L.2
  • 140
    • 0000755273 scopus 로고
    • An overdetermined initial and boundary-value problem for a reaction-diffusion equation
    • 119. A. DE PABLO AND J. L. VAZQUEZ, An overdetermined initial and boundary-value problem for a reaction-diffusion equation, Nonlinear Anal. 19 (1992), 159-269.
    • (1992) Nonlinear Anal. , vol.19 , pp. 159-269
    • De Pablo, A.1    Vazquez, J.L.2
  • 141
    • 0001607121 scopus 로고
    • Diffusion from an instantaneous point source with a concentration-dependent coefficient
    • 120. R. E. PATTLE, Diffusion from an instantaneous point source with a concentration-dependent coefficient, Quart. J. Mech. Appl. Math. 12 (1959), 407-409.
    • (1959) Quart. J. Mech. Appl. Math. , vol.12 , pp. 407-409
    • Pattle, R.E.1
  • 142
    • 0016319291 scopus 로고
    • A necessary and sufficient condition for the existence of an interface in flows through porous media
    • 121. L. A. PELETIER, A necessary and sufficient condition for the existence of an interface in flows through porous media, Arch. Ration. Mech. Anal. 56 (1974), 183-190.
    • (1974) Arch. Ration. Mech. Anal. , vol.56 , pp. 183-190
    • Peletier, L.A.1
  • 143
    • 0011657182 scopus 로고
    • On the existence of an interface in nonlinear diffusion processes
    • "Ordinary and Partial Differential Equations" (B. D. Sleeman and I. M. Michael, Eds.), Springer-Verlag, Berlin
    • 122. L. A. PELETIER, On the existence of an interface in nonlinear diffusion processes, in "Ordinary and Partial Differential Equations" (B. D. Sleeman and I. M. Michael, Eds.), pp.412-416, Lecture Notes in Mathematics, Vol.415, Springer-Verlag, Berlin, 1974.
    • (1974) Lecture Notes in Mathematics , vol.415 , pp. 412-416
    • Peletier, L.A.1
  • 144
    • 0001768828 scopus 로고
    • The porous media equation
    • (H. Amann, N. Bazley, and K. Kirchgässner, Eds.), Pitman, Boston
    • 123. L. A. PELETIER, The porous media equation, in "Applications of Nonlinear Analysis in the Physical Sciences" (H. Amann, N. Bazley, and K. Kirchgässner, Eds.), pp. 229-241, Pitman, Boston, 1981.
    • (1981) Applications of Nonlinear Analysis in the Physical Sciences , pp. 229-241
    • Peletier, L.A.1
  • 145
    • 0011538425 scopus 로고
    • Bounded speed of propagation for solutions to radiative transfer equations
    • 124. B. PERTHAME AND J. L. VAZQUEZ, Bounded speed of propagation for solutions to radiative transfer equations, Comm. Math. Phys. 130 (1990), 457-469.
    • (1990) Comm. Math. Phys. , vol.130 , pp. 457-469
    • Perthame, B.1    Vazquez, J.L.2
  • 146
    • 84951416437 scopus 로고
    • Existence of solutions of quenching problems
    • 125. D. PHILLIPS, Existence of solutions of quenching problems, Appl. Anal. 24 (1987), 253-264.
    • (1987) Appl. Anal. , vol.24 , pp. 253-264
    • Phillips, D.1
  • 148
    • 0011603090 scopus 로고
    • Conditions for space localization of the solutions of the non-linear equation of heat conduction
    • 127. L. D. POKROVSKII AND S. N. TARANENKO, Conditions for space localization of the solutions of the non-linear equation of heat conduction, U.S.S.R. Comput. Math. Math. Phys. 22 (1982), 264-269. Translation of Zh. Vychisl. Mat. Mat. Fiz. 22 (1982), 747-751.
    • (1982) U.S.S.R. Comput. Math. Math. Phys. , vol.22 , pp. 264-269
    • Pokrovskii, L.D.1    Taranenko, S.N.2
  • 149
    • 0011603090 scopus 로고
    • 127. L. D. POKROVSKII AND S. N. TARANENKO, Conditions for space localization of the solutions of the non-linear equation of heat conduction, U.S.S.R. Comput. Math. Math. Phys. 22 (1982), 264-269. Translation of Zh. Vychisl. Mat. Mat. Fiz. 22 (1982), 747-751.
    • (1982) Zh. Vychisl. Mat. Mat. Fiz. , vol.22 , pp. 747-751
  • 150
    • 34247647193 scopus 로고
    • Capillary conduction of liquids through porous mediums
    • 128. L. A. RICHARDS, Capillary conduction of liquids through porous mediums, Physics 1 (1931), 318-333.
    • (1931) Physics , vol.1 , pp. 318-333
    • Richards, L.A.1
  • 151
    • 0001632479 scopus 로고
    • Thermal waves in an absorbing and convecting medium
    • 129. P. ROSENAU AND S. KAMIN, Thermal waves in an absorbing and convecting medium, Phys. D 8 (1983), 273-283.
    • (1983) Phys. D , vol.8 , pp. 273-283
    • Rosenau, P.1    Kamin, S.2
  • 152
    • 0000837295 scopus 로고
    • The initial and boundary value problem for a class of degenerate parabolic equations
    • 130. P. E. SACKS, The initial and boundary value problem for a class of degenerate parabolic equations, Comm. Partial Differential Equations 8 (1983), 693-733.
    • (1983) Comm. Partial Differential Equations , vol.8 , pp. 693-733
    • Sacks, P.E.1
  • 153
    • 0014615845 scopus 로고
    • Free boundary problems of Stephan type with prescribed flux
    • 131. A. SCHATZ, Free boundary problems of Stephan type with prescribed flux, J. Math. Anal. Appl. 28 (1969), 569-580.
    • (1969) J. Math. Anal. Appl. , vol.28 , pp. 569-580
    • Schatz, A.1
  • 154
    • 35949037602 scopus 로고
    • The electrophysics of a nerve fiber
    • 132. A. C. SCOTT, The electrophysics of a nerve fiber, Rev. Modern Phys. 47 (1975), 487-533.
    • (1975) Rev. Modern Phys. , vol.47 , pp. 487-533
    • Scott, A.C.1
  • 155
    • 0011669142 scopus 로고
    • Instantaneous appearance of singularities of a solution of a degenerate parabolic equation
    • 133. S. I. SHMAREV, Instantaneous appearance of singularities of a solution of a degenerate parabolic equation, Siberian Math. J. 31 (1991), 671-682. Translation of Sibirsk. Mat. Zh. 31 (1990), 166-179.
    • (1991) Siberian Math. J. , vol.31 , pp. 671-682
    • Shmarev, S.I.1
  • 156
    • 0011669142 scopus 로고
    • 133. S. I. SHMAREV, Instantaneous appearance of singularities of a solution of a degenerate parabolic equation, Siberian Math. J. 31 (1991), 671-682. Translation of Sibirsk. Mat. Zh. 31 (1990), 166-179.
    • (1990) Sibirsk. Mat. Zh. , vol.31 , pp. 166-179
  • 159
    • 0011659472 scopus 로고
    • Existence, uniqueness and properties of the solutions of a degenerate parabolic equation with diffusion-advection-absorption
    • 136. SONG B., Existence, uniqueness and properties of the solutions of a degenerate parabolic equation with diffusion-advection-absorption, Acta Math. Appl. Sinica (English Ser.) 10 (1994), 113-140.
    • (1994) Acta Math. Appl. Sinica (English Ser.) , vol.10 , pp. 113-140
    • Song, B.1
  • 160
    • 0002536525 scopus 로고
    • The flow of water in unsaturated soils
    • (R. J. M. de Wiest, Ed.), Academic Press, New York
    • 137. D. SWARTZENDRUBER, The flow of water in unsaturated soils, in "Flow through Porous Media" (R. J. M. de Wiest, Ed.), pp. 215-292, Academic Press, New York, 1969.
    • (1969) Flow Through Porous Media , pp. 215-292
    • Swartzendruber, D.1
  • 161
    • 84962767376 scopus 로고
    • Asymptotic behaviour and propagation properties on the one-dimensional flow of gas in a porous medium
    • 138. J. L. VAZQUEZ, Asymptotic behaviour and propagation properties on the one-dimensional flow of gas in a porous medium, Trans. Amer. Math. Soc. 277 (1983), 507-527.
    • (1983) Trans. Amer. Math. Soc. , vol.277 , pp. 507-527
    • Vazquez, J.L.1
  • 162
    • 84968510082 scopus 로고
    • The interfaces of one-dimensional flows in porous media
    • 139. J. L. VAZQUEZ, The interfaces of one-dimensional flows in porous media, Trans. Amer. Math. Soc. 285 (1984), 717-737.
    • (1984) Trans. Amer. Math. Soc. , vol.285 , pp. 717-737
    • Vazquez, J.L.1
  • 163
    • 0000734827 scopus 로고
    • Behaviour of the velocity of one-dimensional flows in porous media
    • 140. J. L. VAZQUEZ, Behaviour of the velocity of one-dimensional flows in porous media, Trans. Amer. Math. Soc. 286 (1984), 787-802.
    • (1984) Trans. Amer. Math. Soc. , vol.286 , pp. 787-802
    • Vazquez, J.L.1
  • 164
    • 84971179878 scopus 로고
    • Regularity of solutions and interfaces of the porous medium equation via local estimates
    • 141. J. L. VAZQUEZ, Regularity of solutions and interfaces of the porous medium equation via local estimates, Proc. Roy. Soc. Edinburgh Sect. A 112 (1989), 1-13.
    • (1989) Proc. Roy. Soc. Edinburgh Sect. A , vol.112 , pp. 1-13
    • Vazquez, J.L.1
  • 165
    • 0000383614 scopus 로고
    • An introduction to the mathematical theory of the porous medium equation
    • (M. C. Delfour and G. Sabidussi, Eds.), Kluwer Academic, Dordrecht
    • 142. J. L. VAZQUEZ, An introduction to the mathematical theory of the porous medium equation, in Shape Optimization and Free Boundaries(M. C. Delfour and G. Sabidussi, Eds.), pp. 347-389, Kluwer Academic, Dordrecht, 1992.
    • (1992) Shape Optimization and Free Boundaries , pp. 347-389
    • Vazquez, J.L.1
  • 166
    • 0002924519 scopus 로고
    • The asymptotic properties of self-modelling solutions of the nonstationary gas filtration equations
    • 143. IA. B. ZEL'DOVICH AND G. I. BARENBLATT, The asymptotic properties of self-modelling solutions of the nonstationary gas filtration equations, Sov. Phys. Dokl. 3 (1958), 44-47. Translation of Dokl. Akad. Nauk SSSR (N.S.) 118 (1958), 671-674.
    • (1958) Sov. Phys. Dokl. , vol.3 , pp. 44-47
    • Zel'Dovich, Ia.B.1    Barenblatt, G.I.2
  • 167
    • 0001319575 scopus 로고
    • 143. IA. B. ZEL'DOVICH AND G. I. BARENBLATT, The asymptotic properties of self-modelling solutions of the nonstationary gas filtration equations, Sov. Phys. Dokl. 3 (1958), 44-47. Translation of Dokl. Akad. Nauk SSSR (N.S.) 118 (1958), 671-674.
    • (1958) Dokl. Akad. Nauk SSSR (N.S.) , vol.118 , pp. 671-674
  • 169
    • 0011663864 scopus 로고
    • 144. Y. B. ZELDOVICH, "Theory of Flame Propagation," National Advisory Committee for Aeronautics Technical Memorandum 1282, 1951. Translation of Zh. Fiz. Khim. 22 (1948), 27-49.
    • (1948) Zh. Fiz. Khim. , vol.22 , pp. 27-49
  • 170
    • 0009000254 scopus 로고
    • On the theory of propagation of heat with the heat conductivity depending upon the temperature
    • "Collection in Honour of the Seventieth Birthday of Academician A. F. Ioffe," In Russian
    • 145. YA. B. ZEL'DOVICH AND A. S. KOMPANEEC, On the theory of propagation of heat with the heat conductivity depending upon the temperature, in "Collection in Honour of the Seventieth Birthday of Academician A. F. Ioffe," pp. 61-71, Iz. Akad. Nauk SSSR Moscow, 1950. [In Russian]
    • (1950) Iz. Akad. Nauk Sssr Moscow , pp. 61-71
    • Zel'Dovich, Ya.B.1    Kompaneec, A.S.2
  • 173
    • 0011538862 scopus 로고
    • Uniqueness of solutions of quasilinear degenerate parabolic equations
    • 148. J. ZHAO, Uniqueness of solutions of quasilinear degenerate parabolic equations, Dongbei Shuxue 1 (1985), 153-165.
    • (1985) Dongbei Shuxue , vol.1 , pp. 153-165
    • Zhao, J.1


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