@article{AIHPC_1987__4_3_203_0, author = {Aronson, D. G. and Vazquez, Juan Luis}, title = {The porous medium equation as a finite-speed approximation to a Hamilton-Jacobi equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {4}, year = {1987}, pages = {203-230}, mrnumber = {898047}, zbl = {0635.35047}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_1987__4_3_203_0} }
Aronson, D. G.; Vazquez, J. L. The porous medium equation as a finite-speed approximation to a Hamilton-Jacobi equation. Annales de l'I.H.P. Analyse non linéaire, Tome 4 (1987) pp. 203-230. http://gdmltest.u-ga.fr/item/AIHPC_1987__4_3_203_0/
[A1] Regularity properties of flows through porous media, SIAM J. Appl. Math., t. 17, 1969, p. 461-467. | MR 247303 | Zbl 0187.03401
,[A 2] Regularity properties of flows through porous media: the interface, Arch. Rational Mech. Anal., t. 37, 1970, p. 1-10. | MR 255996 | Zbl 0202.37901
,[AB] Régularité des solutions de l'équation des milieux poreux dans R", C. R. Acad. Sci. Paris, t. 288, 1979, p. 103-105. | MR 524760 | Zbl 0397.35034
, ,[AC] The initial trace of a solution of the porous medium equation, Trans. Amer. Math. Soc., t. 280, 1983, p. 351-366. | MR 712265 | Zbl 0556.76084
, ,[ACK] How an initially stationary interface begins to move in porous medium flow, SIAM J. Math. Anal., t. 14, 1983, p. 639-658. | MR 704481 | Zbl 0542.76119
, , ,[ACV] Interfaces with a corner-point in one-dimensional porous medium flow, Comm. Pure Applied Math., t. 38, 1985, p. 375-404. | MR 792397 | Zbl 0544.35058
, , ,[BC 1] The continuous dependence on φ of the solutions of ut - Δφ(u) = 0, Indiana Univ. Math. J., t. 30, 1981, p. 161-177. | MR 604277 | Zbl 0482.35012
, ,[BC2] Regularizing effects of homogeneous evolution equations, Contributions to Analysis and Geometry, Supplement to American J. Math., D. N. Clark et al. eds., Baltimore, 1981, p. 23-39. | MR 648452 | Zbl 0556.35067
, ,[BCP] Solutions of the porous medium equation in R'' under optimal conditions on initial values, Indiana Univ. Math. J., t. 33, 1984, p. 51-87. | MR 726106 | Zbl 0552.35045
, , ,[BV] Concavity of solutions of the porous medium equation, to appear in Trans. Amer. Math. Soc. | MR 869400 | Zbl 0628.76092
, ,[B] The Hamilton-Jacobi equation : a global approach, Academic Press, New York, 1977. | MR 442431 | Zbl 0418.49001
,[CF] Regularity of the free-boundary for the one-dimensional flow of gas in a porous medium, Amer. J. Math., t. 101, 1979, p. 1193-1218. | MR 548877 | Zbl 0439.76084
, ,[CEL] Some properties of viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., t. 282, 1984, p. 487-502. | MR 732102 | Zbl 0543.35011
, , ,[CL] Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., t. 277, 1983, p. 1-42. | MR 690039 | Zbl 0599.35024
, ,[D] Characteristics in hyperbolic conservation laws in Nonlinear Analysis and Mechanics, Vol. I, ed. R. J. Knops, London, Pitman, 1977, p. 1-58. | MR 481581 | Zbl 0373.35048
,[DK] Nonnegative solutions of the porous medium equation, Comm. Partial Diff. Equations, t. 9, 1984, p. 409-437. | MR 741215 | Zbl 0547.35057
, ,[G] Hölder continuity of solutions of parabolic equations, J. London Math. Soc., t. 13, 1976, p. 103-106. | MR 399658 | Zbl 0319.35045
,[GJ] A finite-different approach to some degenerate non-linear parabolic equations, SIAM J. Appl. Math., t. 20, 1971, p. 199-223. | MR 290600 | Zbl 0226.65065
, ,[HP] The Cauchy problem for ut = Δum when 0 < m < 1, Trans. Amer. Math. Soc., t. 290, 1985, p. 1-14.
, ,[H] The partial differential equation ut + uux = μuxx. Comm. Pure Applied Math., t. 3, 1950, p. 201-230. | MR 47234 | Zbl 0039.10403
,[K] The asymptotic behaviour of the solution of the filtration equation, Israel J. Math., t. 14, 1973, p. 76-78. | MR 315292 | Zbl 0254.35054
,[KC] Waiting time behaviour in a nonlinear diffusion equation. Studies in Applied Maths., t. 67, 1982, p. 79-105. | MR 670736 | Zbl 0499.76078
, ,[Kn] The porous medium equation in one dimension, Trans. Amer. Math. Soc., t. 234, 1977, p. 381-415. | MR 492856 | Zbl 0365.35030
,[La] Hyperbolic systems of conservation laws II, Comm. Pure Applied Math., t. 10, 1957, p. 537-566. | MR 93653 | Zbl 0081.08803
,[Li] Generalized solutions of Hamilton-Jacobi equations, Research Notes in Math. # 69, Pitman, Boston, 1982. | MR 667669 | Zbl 0497.35001
,[LSV] In preparation.
, , ,[LP] Source-solutions and asymptotic behavior in conservation laws, J. Diff. Equations, t. 51, 1984, p. 419-441. | MR 735207 | Zbl 0545.35057
, ,[O] Discontinuous solutions of nonlinear differential equations, Amer. Math. Soc. Translations, t. 26, (2), 1983, p. 95-172. Doklady Akad. Nauk SSSR, t. 109, 1956, p. 1098-1101 (in Russian). | MR 83088 | Zbl 0131.31803
,[OKC] The Cauchy problem and boundary problems for equations of the type of nonstationary filtration, lzv. Akad. Nauk SSSR Ser. Mat., t. 22, 1958, p. 667-704 (in Russian). | MR 99834
, , ,[V1] Asymptotic behaviour and propagation properties of the one-dimensional flow of a gas in a porous medium, Trans. Amer. Math. Soc., t. 277, 1983, p. 505-527. | MR 694373 | Zbl 0528.76096
,[V2] Behaviour of the velocity of one-dimensional flows in porous media, Trans. Amer. Math. Soc., t. 286, 1984, p. 787-802. | MR 760987 | Zbl 0524.35014
,[V3] The interfaces of one-dimensional flows in porous media, Trans. Amer. Math. Soc., t. 285, 1984, p. 717-737. | MR 752500 | Zbl 0524.35060
,