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Volumn 9, Issue 3, 1998, Pages 327-350

Evolution of self-similarity, and other properties of waiting-time solutions of the porous medium equation: The case of viscous gravity currents

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EID: 0032368382     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S095679259700329X     Document Type: Article
Times cited : (9)

References (39)
  • 1
    • 0014847244 scopus 로고
    • Regularity properties of flows through porous media: A counterexample
    • ARONSON, D. G. (1970) Regularity properties of flows through porous media: A counterexample. SIAM J. Appl. Math., 19, 299-307.
    • (1970) SIAM J. Appl. Math. , vol.19 , pp. 299-307
    • Aronson, D.G.1
  • 2
    • 0000843007 scopus 로고
    • Calculation of anomalous exponents in nonlinear diffusion
    • ARONSON, D. G. & VÁZQUEZ, J. L. (1994) Calculation of anomalous exponents in nonlinear diffusion. Phys. Rev. Lett., 72, 348-351.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 348-351
    • Aronson, D.G.1    Vázquez, J.L.2
  • 3
    • 0040430170 scopus 로고
    • How an initially stationary interface begins to move in porous medium flow 1983
    • ARONSON, D. G., CAFFARELLI, L. A. & KAMIN, S. (1983) How an initially stationary interface begins to move in porous medium flow 1983. SIAM J. Math. Anal., 14, 639-658.
    • (1983) SIAM J. Math. Anal. , vol.14 , pp. 639-658
    • Aronson, D.G.1    Caffarelli, L.A.2    Kamin, S.3
  • 4
    • 84990602592 scopus 로고
    • Interfaces with a corner point in one-dimensional porous medium flow
    • ARONSON, D. G., CAFFARELLI, L. A. & VÁZQUEZ, J. L. (1985) Interfaces with a corner point in one-dimensional porous medium flow. Comm. Pure Appl. Math., 38, 375-404.
    • (1985) Comm. Pure Appl. Math. , vol.38 , pp. 375-404
    • Aronson, D.G.1    Caffarelli, L.A.2    Vázquez, J.L.3
  • 5
    • 0003004337 scopus 로고
    • One some unsteady motions of fluids and gases in a porous medium
    • BARENBLATT, G. I. (1952) One some unsteady motions of fluids and gases in a porous medium. Prikl. Mat. i Mekh., 16(1), 67-78.
    • (1952) Prikl. Mat. i Mekh. , vol.16 , Issue.1 , pp. 67-78
    • Barenblatt, G.I.1
  • 7
    • 0011468611 scopus 로고
    • On the dipole-type solution in problems of unsteady gas filtration in the polytropic regime
    • BARENBLATT, G. I. & ZEL'DOVICH, YA. B. (1957) On the dipole-type solution in problems of unsteady gas filtration in the polytropic regime. Prikl. Mat. i Mekh., 21, 718-720.
    • (1957) Prikl. Mat. i Mekh. , vol.21 , pp. 718-720
    • Barenblatt, G.I.1    Zel'dovich, Ya.B.2
  • 8
    • 0000885949 scopus 로고
    • Self-similar solutions as intermediate asymptotics
    • BARENBLATT, G. I. & ZEL'DOVICH, YA. B. (1972) Self-similar solutions as intermediate asymptotics. Ann. Rev. Fluid Mech., 4, 295-312.
    • (1972) Ann. Rev. Fluid Mech. , vol.4 , pp. 295-312
    • Barenblatt, G.I.1    Zel'dovich, Ya.B.2
  • 9
    • 0017768062 scopus 로고
    • Viscous sheets advancing over dry beds
    • BUCKMASTER, J. (1977) Viscous sheets advancing over dry beds. J. Fluid Mech., 81, 735-756.
    • (1977) J. Fluid Mech. , vol.81 , pp. 735-756
    • Buckmaster, J.1
  • 10
    • 85034472762 scopus 로고
    • Numerical solutions of viscous, waiting, gravity driven flows
    • CIC
    • DEL CARMEN, A. & FERRERI, J. C. (1995) Numerical solutions of viscous, waiting, gravity driven flows. Física de Fluidos 95, 113-127. CIC.
    • (1995) Física de Fluidos , vol.95 , pp. 113-127
    • Del Carmen, A.1    Ferreri, J.C.2
  • 12
    • 0016986163 scopus 로고
    • On a class of similarity solutions of the porous media equations
    • GILDING, B. H. & PELETIER, L. A. (1977a) On a class of similarity solutions of the porous media equations. J. Math. Anal. Appl., 55, 351-364.
    • (1977) J. Math. Anal. Appl. , vol.55 , pp. 351-364
    • Gilding, B.H.1    Peletier, L.A.2
  • 13
    • 0017474040 scopus 로고
    • On a class of similarity solutions of the porous media equations II
    • GILDING, B. H. & PELETIER, L. A. (1977b) On a class of similarity solutions of the porous media equations II. J. Math. Anal. Appl., 57, 522-538.
    • (1977) J. Math. Anal. Appl. , vol.57 , pp. 522-538
    • Gilding, B.H.1    Peletier, L.A.2
  • 14
    • 85034469610 scopus 로고
    • Asintótica autosemejante de flujos viscogravitatorios con tiempo de espera en función del perfil inicial
    • GRATTON, J. & VIGO, C. (1994a) Asintótica autosemejante de flujos viscogravitatorios con tiempo de espera en función del perfil inicial. Anales AFA, 6, 315-319.
    • (1994) Anales AFA , vol.6 , pp. 315-319
    • Gratton, J.1    Vigo, C.2
  • 15
    • 85034459386 scopus 로고
    • Soluciones autosemejantes con tiempo de espera de ecuaciones no lineales de difusión
    • GRATTON, J. & VIGO, C. (1994b) Soluciones autosemejantes con tiempo de espera de ecuaciones no lineales de difusión. Anales AFA, 6, 326-331.
    • (1994) Anales AFA , vol.6 , pp. 326-331
    • Gratton, J.1    Vigo, C.2
  • 16
    • 0025240137 scopus 로고
    • Self-similar viscous gravity currents: Phase plane formalism
    • GRATTON, J. & MINOTTI, F. (1990) Self-similar viscous gravity currents: phase plane formalism. J. Fluid Mech., 210, 155-182.
    • (1990) J. Fluid Mech. , vol.210 , pp. 155-182
    • Gratton, J.1    Minotti, F.2
  • 18
    • 0018534253 scopus 로고
    • Similarity solutions of the nonlinear diffusion equation
    • GRUNDY, R. E. (1979) Similarity solutions of the nonlinear diffusion equation. Quart. Appl. Math., 37, 259-280.
    • (1979) Quart. Appl. Math. , vol.37 , pp. 259-280
    • Grundy, R.E.1
  • 19
    • 0542387619 scopus 로고
    • A general corrective procedure for the numerical solution of initial-value problems
    • HIRT, C. W. & HARLOW, F. (1967) A general corrective procedure for the numerical solution of initial-value problems. J. Comp. Phys., 2, 114-119.
    • (1967) J. Comp. Phys. , vol.2 , pp. 114-119
    • Hirt, C.W.1    Harlow, F.2
  • 20
    • 0020335797 scopus 로고
    • The propagation of two-dimensional viscous gravity currents over a rigid horizontal surface
    • HUPPERT, H. E. (1982) The propagation of two-dimensional viscous gravity currents over a rigid horizontal surface. J. Fluid Mech., 121, 43-58.
    • (1982) J. Fluid Mech. , vol.121 , pp. 43-58
    • Huppert, H.E.1
  • 21
    • 0001172369 scopus 로고
    • On the use of nonuniform grids in finite-difference equations
    • KÁLNAY DE RIVAS, E. (1972) On the use of nonuniform grids in finite-difference equations. J. Comp. Phys., 10, 201-203.
    • (1972) J. Comp. Phys. , vol.10 , pp. 201-203
    • Kálnay De Rivas, E.1
  • 22
    • 0542411203 scopus 로고
    • Continuous groups of transformations of differential equations; applications to free boundary problems
    • E. Magenes (ed.), Tecnoprint, Roma
    • KAMIN, S. (1980) Continuous groups of transformations of differential equations; applications to free boundary problems. In E. Magenes (ed.), Free Boundary Problems, Tecnoprint, Roma.
    • (1980) Free Boundary Problems
    • Kamin, S.1
  • 23
    • 0020190477 scopus 로고
    • Waiting-time behavior in a nonlinear diffusion equation
    • KATH, W. L. & COHEN, D. S. (1982) Waiting-time behavior in a nonlinear diffusion equation. Stud. Appl. Math., 67, 79-105.
    • (1982) Stud. Appl. Math. , vol.67 , pp. 79-105
    • Kath, W.L.1    Cohen, D.S.2
  • 24
    • 84968487166 scopus 로고
    • The porous medium equation in one dimension
    • KNERR, B. F. (1977) The porous medium equation in one dimension. Trans. Am. Math. Soc., 234, 381-415.
    • (1977) Trans. Am. Math. Soc. , vol.234 , pp. 381-415
    • Knerr, B.F.1
  • 25
    • 0039949243 scopus 로고
    • Initial motion of the free boundary for a non-linear diffusion equation
    • LACEY, A. A. (1983) Initial motion of the free boundary for a non-linear diffusion equation. IMA J. Appl. Math., 31, 113-119.
    • (1983) IMA J. Appl. Math. , vol.31 , pp. 113-119
    • Lacey, A.A.1
  • 26
    • 0001072629 scopus 로고
    • "Waiting-time" solutions of a nonlinear diffusion equation
    • LACEY, A. A., OCKENDON, J. R. & TAYLER, A. B. (1982) "Waiting-time" solutions of a nonlinear diffusion equation. J. Appl. Math., 42, 1252-1264.
    • (1982) J. Appl. Math. , vol.42 , pp. 1252-1264
    • Lacey, A.A.1    Ockendon, J.R.2    Tayler, A.B.3
  • 27
    • 0019073745 scopus 로고
    • Asymptotic analysis of nonlinear Marshak waves
    • LARSEN, E. W. & POMRANING, G. C. (1980) Asymptotic analysis of nonlinear Marshak waves. SIAM J. Appl. Math., 39, 201-212.
    • (1980) SIAM J. Appl. Math. , vol.39 , pp. 201-212
    • Larsen, E.W.1    Pomraning, G.C.2
  • 28
    • 25544437482 scopus 로고
    • Waiting time solutions of a non-linear diffusion equation: Experimental study of a creeping flow near a waiting front
    • in press
    • MARINO, B. M., THOMAS, L. P., GRATTON, R., DIEZ, J. A., BETELÚ, S. & GRATTON, J. (1995) Waiting time solutions of a non-linear diffusion equation: experimental study of a creeping flow near a waiting front. Phys. Rev. E (in press).
    • (1995) Phys. Rev. E
    • Marino, B.M.1    Thomas, L.P.2    Gratton, R.3    Diez, J.A.4    Betelú, S.5    Gratton, J.6
  • 29
    • 0001920493 scopus 로고
    • Effect of radiation on shock wave behavior
    • MARSHAK, R. E. (1958) Effect of radiation on shock wave behavior. Phys. Fluids, 1, 24-29.
    • (1958) Phys. Fluids , vol.1 , pp. 24-29
    • Marshak, R.E.1
  • 31
    • 0001607121 scopus 로고
    • Diffusion from an instantaneous point source with a concentration-dependent coefficient
    • PATTLE, R. E. (1959) Diffusion from an instantaneous point source with a concentration-dependent coefficient. Quart. J. Mech. Appl. Math., 12, 407-409.
    • (1959) Quart. J. Mech. Appl. Math. , vol.12 , pp. 407-409
    • Pattle, R.E.1
  • 33
    • 0345254006 scopus 로고
    • A class of similar solutions of the non-linear diffusion equation
    • PERT, G. J. (1977) A class of similar solutions of the non-linear diffusion equation. J. Phys. A: Math. Gen., 10(4), 583-593.
    • (1977) J. Phys. A: Math. Gen. , vol.10 , Issue.4 , pp. 583-593
    • Pert, G.J.1
  • 36
    • 84972517979 scopus 로고
    • Numerical approximations to interface curves for a porous media equation
    • TOMOEDA, K. & MIMURA, M. (1983) Numerical approximations to interface curves for a porous media equation. Hiroshima Math. J., 13, 273-294.
    • (1983) Hiroshima Math. J. , vol.13 , pp. 273-294
    • Tomoeda, K.1    Mimura, M.2
  • 37
    • 25544471910 scopus 로고
    • Large time behavior of the solutions of the one-dimensional porous media equation
    • Pitman, Boston
    • VÁZQUEZ, J. L. (1983) Large time behavior of the solutions of the one-dimensional porous media equation. Free Boundary Problems: Theory and Applications, Vol. I. Pitman, Boston, pp. 167-177.
    • (1983) Free Boundary Problems: Theory and Applications , vol.1 , pp. 167-177
    • Vázquez, J.L.1
  • 38
    • 84968510082 scopus 로고
    • The interface of one-dimensional flows in porous media
    • VÁZQUEZ, J. L. (1984) The interface of one-dimensional flows in porous media. Trans. Amer. Math. Soc., 285, 717-737.
    • (1984) Trans. Amer. Math. Soc. , vol.285 , pp. 717-737
    • Vázquez, J.L.1


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