메뉴 건너뛰기




Volumn 197, Issue 5-6, 2006, Pages 753-790

Asymptotic behaviour of supports of solutions of quasilinear many-dimensional parabolic equations of non-stationary diffusion-convection type

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33748805272     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2006v197n05ABEH003777     Document Type: Article
Times cited : (7)

References (34)
  • 1
    • 0001217997 scopus 로고
    • Cauchy problem and boundary-value problems for equations of non-stationary filtration type
    • Russian
    • O. A. Oleǐnik, A. S. Kalashnikov, and Chou Yu-lin, "Cauchy problem and boundary-value problems for equations of non-stationary filtration type", Izv. Akad. Nauk SSSR Ser. Mat. 22:5 (1958), 667-704. (Russian)
    • (1958) Izv. Akad. Nauk SSSR Ser. Mat. , vol.22 , Issue.5 , pp. 667-704
    • Oleǐnik, O.A.1    Kalashnikov, A.S.2    Chou, Y.-L.3
  • 2
    • 0000467105 scopus 로고
    • Some problems of the qualitative theory of nonlinear degenerate second-order parabolic equations
    • A. S. Kalashnikov, "Some problems of the qualitative theory of nonlinear degenerate second-order parabolic equations", Uspekhi Mat. Nauk 42:2 (1987), 135-176;
    • (1987) Uspekhi Mat. Nauk , vol.42 , Issue.2 , pp. 135-176
    • Kalashnikov, A.S.1
  • 3
    • 84862599035 scopus 로고
    • English transl
    • English transl, in Russian Math. Surveys 42:2 (1987), 169-222.
    • (1987) Russian Math. Surveys , vol.42 , Issue.2 , pp. 169-222
  • 5
    • 0011605815 scopus 로고
    • The nature of the propagation of perturbations in processes described by quasilinear parabolic equations
    • Moscow State University, Moscow. (Russian)
    • A. S. Kalashnikov, "The nature of the propagation of perturbations in processes described by quasilinear parabolic equations", Trudy Sem. Petrovsk., Moscow State University, Moscow 1975, pp. 135-144. (Russian)
    • (1975) Trudy Sem. Petrovsk. , pp. 135-144
    • Kalashnikov, A.S.1
  • 6
    • 0017139285 scopus 로고
    • The Cauchy problem for an equation in the theory of infiltration
    • B. H. Gilding and L. A. Peletier, "The Cauchy problem for an equation in the theory of infiltration", Arch. Rational. Mech. Anal. 61 (1976), 127-140.
    • (1976) Arch. Rational. Mech. Anal. , vol.61 , pp. 127-140
    • Gilding, B.H.1    Peletier, L.A.2
  • 7
    • 38249034235 scopus 로고
    • On a nonlinear degenerate parabolic equation in infiltration or evaporation through a porous medium
    • 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
  • 8
    • 0001279719 scopus 로고
    • Improved theory for a nonlinear degenerate parabolic equation
    • B. H. Gilding, "Improved theory for a nonlinear degenerate parabolic equation", Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 16:2 (1989), 165-224.
    • (1989) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.16 , Issue.2 , pp. 165-224
    • Gilding, B.H.1
  • 10
    • 0002002430 scopus 로고
    • Non-linear elliptic and parabolic equations
    • VINITI, Moscow. (Russian)
    • Yu. A. Dubinskiǐ, "Non-linear elliptic and parabolic equations", Sovrem. Problemy Mat, vol. 9, VINITI, Moscow 1976, pp. 5-130. (Russian)
    • (1976) Sovrem. Problemy Mat , vol.9 , pp. 5-130
    • Dubinskiǐ, Yu.A.1
  • 11
    • 0002973412 scopus 로고
    • Sur la résolution d'une équation et d'une inéquation paraboliques non linéaires
    • O. Grange and F. Mignot, "Sur la résolution d'une équation et d'une inéquation paraboliques non liné aires", J. Funct. Anal. 11:1 (1972), 77-92.
    • (1972) J. Funct. Anal. , vol.11 , Issue.1 , pp. 77-92
    • Grange, O.1    Mignot, F.2
  • 12
    • 0001433601 scopus 로고
    • Existence results for doubly nonlinear higher order parabolic equations on unbounded domains
    • F. Bernis, "Existence results for doubly nonlinear higher order parabolic equations on unbounded domains", Math. Ann. 279:3 (1988), 373-394.
    • (1988) Math. Ann. , vol.279 , Issue.3 , pp. 373-394
    • Bernis, F.1
  • 13
    • 0000836987 scopus 로고
    • Quasilinear elliptic-parabolic differential equations
    • 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
  • 14
    • 0000013866 scopus 로고    scopus 로고
    • On mild and weak solutions of elliptic-parabolic problems
    • P. Benilan and P. Wittbold, "On mild and weak solutions of elliptic-parabolic problems", Adv. Differential Equations 1:6 (1996), 1053-1073.
    • (1996) Adv. Differential Equations , vol.1 , Issue.6 , pp. 1053-1073
    • Benilan, P.1    Wittbold, P.2
  • 15
    • 0011668454 scopus 로고
    • On the initial growth of the interfaces in nonlinear diffusion-convection processes
    • (W.-M. Ni, L. A. Peletier, J. Serrin, eds.), Springer-Verlag, New York
    • L. Alvarez, J. I. Diaz, and R. Kersner, "On the initial growth of the interfaces in nonlinear diffusion-convection processes", Nonlinear diffusion equations and their equilibrium, states. I (W.-M. Ni, L. A. Peletier, J. Serrin, eds.), Springer-Verlag, New York 1987, pp. 1-20.
    • (1987) Nonlinear Diffusion Equations and Their Equilibrium, States. I , pp. 1-20
    • Alvarez, L.1    Diaz, J.I.2    Kersner, R.3
  • 16
    • 0002350444 scopus 로고
    • Sufficient and necessary initial mass conditions for the existence of a waiting time in nonlinear-convection processes
    • L. Alvarez and J. I. Diaz, "Sufficient and necessary initial mass conditions for the existence of a waiting time in nonlinear-convection processes", J. Math. Anal. Appl. 155 (1991), 378-393.
    • (1991) J. Math. Anal. Appl. , vol.155 , pp. 378-393
    • Alvarez, L.1    Diaz, J.I.2
  • 17
    • 0017728713 scopus 로고
    • Properties of solutions of an equation in the theory of infiltration
    • 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
  • 18
    • 0000943090 scopus 로고
    • Asymptotic solution of a model nonlinear convective diffusion equation
    • R. E. Grundy, "Asymptotic solution of a model nonlinear 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
  • 21
    • 0011599554 scopus 로고
    • Non existence d'une des frontières libres dans une équation dégénérée en théorie de la filtration
    • J. I. Diaz and R. Kersner, "Non existence d'une des frontières libres dans une équation dégéné rée en théorie de la filtration", C. R. Acad. Sci. Paris Ser. I Math. 296 (1983), 505-508.
    • (1983) C. R. Acad. Sci. Paris Ser. I Math. , vol.296 , pp. 505-508
    • Diaz, J.I.1    Kersner, R.2
  • 22
    • 0002483505 scopus 로고
    • The occurrence of interfaces in nonlinear diffusion-advection processes
    • B. H. Gilding, "The occurrence of interfaces in nonlinear diffusion-advection processes", Arch. Rational Mech. Anal. 100:3 (1988), 243-263.
    • (1988) Arch. Rational Mech. Anal. , vol.100 , Issue.3 , pp. 243-263
    • Gilding, B.H.1
  • 23
    • 84966220953 scopus 로고
    • Instantaneous shrinking in nonlinear diffusion-convection
    • B. H. Gilding and R. Kersner, "Instantaneous shrinking in nonlinear diffusion-convection", Proc. Amer. Math. Soc. 109:2 (1990), 385-394.
    • (1990) Proc. Amer. Math. Soc. , vol.109 , Issue.2 , pp. 385-394
    • Gilding, B.H.1    Kersner, R.2
  • 24
    • 3042557128 scopus 로고    scopus 로고
    • Instantaneous shrinking phenomenon for solutions of higher-dimensional nonlinear diffusion-convection equations
    • A. E. Shishkov, "Instantaneous shrinking phenomenon for solutions of higher-dimensional nonlinear diffusion-convection equations", Methods Funct. Anal. Topology 5:3 (1999), 54-76.
    • (1999) Methods Funct. Anal. Topology , vol.5 , Issue.3 , pp. 54-76
    • Shishkov, A.E.1
  • 25
    • 38249015378 scopus 로고
    • The one-dimensional porous medium equation with convection: Continuous differentiability of interfaces after the waiting time
    • 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. 5:1 (1992), 59-62.
    • (1992) Appl. Math. Lett. , vol.5 , Issue.1 , pp. 59-62
    • Guedda, M.1    Hilhorst, D.2    Picard, C.3
  • 26
    • 0034420827 scopus 로고    scopus 로고
    • Finite speed of propagation for the porous media equation with lower order terms
    • S. Bonafede, G. R. Cirmi, and A. F. Tedeev, "Finite speed of propagation for the porous media equation with lower order terms", Discrete Contin, Dynam. Systems 6:2 (2000), 305-314.
    • (2000) Discrete Contin, Dynam. Systems , vol.6 , Issue.2 , pp. 305-314
    • Bonafede, S.1    Cirmi, G.R.2    Tedeev, A.F.3
  • 27
    • 85164634781 scopus 로고    scopus 로고
    • Propagation of supports of solutions of equations of the kind of many-dimensional non-linear diffusion-convection
    • Russian
    • B. H. Gilding and A. E. Shishkov, "Propagation of supports of solutions of equations of the kind of many-dimensional non-linear diffusion-convection", Uspekhi Mat. Nauk 53:4 (1998), 142. (Russian)
    • (1998) Uspekhi Mat. Nauk , vol.53 , Issue.4 , pp. 142
    • Gilding, B.H.1    Shishkov, A.E.2
  • 28
    • 33646398240 scopus 로고    scopus 로고
    • Propagation of perturbations in quasilinear multidimensional parabolic equations with convective term
    • D. A. Sapronov and A. E. Shishkov, "Propagation of perturbations in quasilinear multidimensional parabolic equations with convective term", Ukrain. Math. Zh. 53:7 (2001), 953-969;
    • (2001) Ukrain. Math. Zh. , vol.53 , Issue.7 , pp. 953-969
    • Sapronov, D.A.1    Shishkov, A.E.2
  • 29
    • 33646398240 scopus 로고    scopus 로고
    • English transl.
    • English transl. in Ukrainian Math. J. 53:7 (2001), 1134-1155.
    • (2001) Ukrainian Math. J. , vol.53 , Issue.7 , pp. 1134-1155
  • 30
    • 84972496033 scopus 로고
    • Weakly nonlinear large time behavior in scalar convection-diffusion equations
    • E. Zuazua, "Weakly nonlinear large time behavior in scalar convection-diffusion equations", Differential Integral Equations 6:6 (1993), 1481-1491.
    • (1993) Differential Integral Equations , vol.6 , Issue.6 , pp. 1481-1491
    • Zuazua, E.1
  • 31
    • 0040249541 scopus 로고
    • Large time behaviour for the heat equation with absorption and convection
    • S. Claudi and F. R. Guarguaglini, "Large time behaviour for the heat equation with absorption and convection", Adv. in Appl. Math. 16:4 (1995), 377-401.
    • (1995) Adv. in Appl. Math. , vol.16 , Issue.4 , pp. 377-401
    • Claudi, S.1    Guarguaglini, F.R.2
  • 32
    • 0000324185 scopus 로고
    • Qualitative properties for some nonlinear higher order degenerate parabolic equations
    • F. Bernis, "Qualitative properties for some nonlinear higher order degenerate parabolic equations", Houston J. Math. 14:3 (1988), 319-352.
    • (1988) Houston J. Math. , vol.14 , Issue.3 , pp. 319-352
    • Bernis, F.1
  • 33
    • 0000761859 scopus 로고
    • An analogue of Saint-Venant's principle and the uniqueness of solutions of boundary value problems for parabolic equations in unbounded domains
    • O. A. Oleinik and G. A. Iosif'yan, "An analogue of Saint-Venant's principle and the uniqueness of solutions of boundary value problems for parabolic equations in unbounded domains", Uspekhi Mat. Nauk 31:6 (1976), 142-166;
    • (1976) Uspekhi Mat. Nauk , vol.31 , Issue.6 , pp. 142-166
    • Oleinik, O.A.1    Iosif'yan, G.A.2
  • 34
    • 84952404838 scopus 로고
    • English transl.
    • English transl. in Russian Math. Surveys 31:6 (1976), 153-178.
    • (1976) Russian Math. Surveys , vol.31 , Issue.6 , pp. 153-178


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.