Asymptotic behaviour of the porous media equation in an exterior domain
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 2, pp. 183-227.
@article{ASNSP_1999_4_28_2_183_0,
     author = {Quir\'os, Fernando and Vazquez, Juan Luis},
     title = {Asymptotic behaviour of the porous media equation in an exterior domain},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {183--227},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 28},
     number = {2},
     year = {1999},
     mrnumber = {1736227},
     zbl = {01417293},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1999_4_28_2_183_0/}
}
TY  - JOUR
AU  - Quirós, Fernando
AU  - Vazquez, Juan Luis
TI  - Asymptotic behaviour of the porous media equation in an exterior domain
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1999
SP  - 183
EP  - 227
VL  - 28
IS  - 2
PB  - Scuola normale superiore
UR  - http://www.numdam.org/item/ASNSP_1999_4_28_2_183_0/
LA  - en
ID  - ASNSP_1999_4_28_2_183_0
ER  - 
%0 Journal Article
%A Quirós, Fernando
%A Vazquez, Juan Luis
%T Asymptotic behaviour of the porous media equation in an exterior domain
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1999
%P 183-227
%V 28
%N 2
%I Scuola normale superiore
%U http://www.numdam.org/item/ASNSP_1999_4_28_2_183_0/
%G en
%F ASNSP_1999_4_28_2_183_0
Quirós, Fernando; Vazquez, Juan Luis. Asymptotic behaviour of the porous media equation in an exterior domain. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 28 (1999) no. 2, pp. 183-227. http://www.numdam.org/item/ASNSP_1999_4_28_2_183_0/

[Ar] D.G. Aronson, The porous medium equation, in "Nonlinear Diffusion Problems" (A. Fasano and M. Primicerio, eds) Lecture Notes in Mathematics 1224, Springer-Verlag, New York, 1986, pp. 1-46. | MR | Zbl

[ACP] D.G. Aronson - M.G. Crandall - L.A. Peletier, Stabilization of solutions of a degenerate nonlinear diffusion problem, Nonlinear Anal. 6 n. 10 (1982), 1001-1022. | MR | Zbl

[AGV] D.G. Aronson - O. Gil - J.L. Vazquez, Limit behaviour of focusing solutions to nonlinear diffusions, Comm. Partial Differential Equations 23 n. 1, 2 (1998), 307-332. | MR | Zbl

[AG] D.G. Aronson - J. Graveleau, A selfsimilar solution to the focusing problem for the porous medium equation, Euro. J. Appl. Math. 4 (1992), 65-81. | MR | Zbl

[AtP] F.V. Atkinson - L.A. Peletier, Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971), 369-379. | MR | Zbl

[Ba] G.I. Barenblatt, On some unsteady motions of a liquid or a gas in a porous medium, Prikl. Mat. Mekh. 16 (1952), 67-78 (in Russian). | MR | Zbl

[Ba2] G.I. Barenblatt, A class of exact solutions of the planar one-dimensional problem of non-stationary gas filtration in a porous medium, Prikl. Mat. Mekh. 17 n. 6 (1953), 739-742 (in Russian). | MR | Zbl

[BV] G.I. Barenblatt - J.L. Vazquez, On a new free boundary problem for unsteady flows in porous media, Euro. J. Appl. Math. 9 (1998), 37-54. | MR | Zbl

[Be] J. Bear, "Dynamics of Fluids in Porous Media", Elsevier, New York, 1971.

[dB] E. Di Benedetto, Continuity of weak solutions to a general porous media equation, Indiana Univ. Math. J. 32 (1983), 83-118. | MR | Zbl

[Bn] Ph. Bénilan, "Equations d'évolution dans un espace de Banach quelconque et applications", Thèse Orsay, 1972.

[BC] Ph. Bénilan - M.G. Crandall, The continuous dependence on ϕ of solutions of ut - Δϕ(u) = 0, Indiana Univ. Math. J. 30 (1981), 161-177. | Zbl

[BHV] F. Bernis - J. Hulshof - J.L. Vázquez, A very singular solution for the dual porous media equation and the asymptotic behaviour of general solutions, J. Reine Angew. Math. 435 (1993), 1-31. | MR | Zbl

[Br] M. Bertsch, A class of degenerate diffusion equations with a singular nonlinear term, Nonlinear Anal. 7 n. 1 (1983), 117-127. | MR | Zbl

[C] J. Carr, "Applications of Centre Manifold Theory", Springer-Verlag, New York, 1981. | MR | Zbl

[GV] V.A. Galaktionov - J.L. Vázquez, Asymptotic behaviour of nonlinear parabolic equations with critical exponents. A dynamical systems approach, J. Funct. Anal. 100 (1991), 435-462. | MR | Zbl

[Gi] B.H. Gilding, On a class of similarity solutions of the porous media equation III, J. Math. Anal. Appl. 77 (1980), 381-402. | MR | Zbl

[GP1] B.H. Gilding - L.A. Peletier, On a class of similarity solutions of the porous media equation, J. Math. Anal. Appl. 55 (1976), 351-364. | MR | Zbl

[GP2] B.H. Gilding - L.A. Peletier, On a class of similarity solutions of the porous media equation II, J. Math. Anal. Appl. 57 (1977), 522-538. | MR | Zbl

[G4] J. Goncerzewicz - H. Marcinkowska - W. Okrasinski - K. Tabisz, On the percolation of water from a cylindrical reservoir into the surrounding soil, Zastosow. Mat. 16 (1978), 249-261. | MR | Zbl

[GO] J. Goncerzewicz - W. Okrasinski, A lower estimate of the interface of some nonlinear diffusion problems, Extracta Math. 9 (1994), 95-100. | MR | Zbl

[H] J. Hulshof, Similarity solutions of the porous medium equation with sign changes, J. Math. Anal. Appl. 157 n. 1 (1991), 75-111. | MR | Zbl

[HV] J. Hulshof - J.L. Vázquez, The dipole solution for the porous medium equation in several space dimensions, Annali Scuola Norm. Sup. Pisa Cl. Sc. 20 (1993), 193-217. | Numdam | MR | Zbl

[J] C.W. Jones, On reducible nonlinear differential equations occurring in mechanics, Proc. Roy. Soc. A217 (1953), 327-343. | MR | Zbl

[LOT] A.A. Lacey - J.R. Ockendon - A.B. Tayler, "Waiting-time" solutions of a nonlinear diffusion equation, SIAM J. Appl. Math. 42 (1982), 1252-1264. | MR | Zbl

[M] M. Muskat, "The Flow of Homogeneous Fluids Through Porous Media", McGraw-Hill, New York, 1937. | JFM

[O] W. Okrasinski, Asymptotic behaviour of the free boundary of some nonlinear diffusion problems, Math. Models Methods Appl. Sci. 19 (1996), 375-380. | MR | Zbl

[P] L.A. Peletier, Asymptotic behavior of solutions of the porous media equation, SIAM J. Appl. Math. 21 n. 4 (1971), 542-551. | MR | Zbl

[PK] P. Ya. Polubarinova-Kochina, On a nonlinear differential equation encountered in the theory of infiltration, Dokl. Akad. Nauk UZSSR 63 n. 6 (1948), 623-627.

[QV] F. Quirós - J.L. Vázquez, Asymptotic convergence of the Stefan problem to Hele-Shaw, Trans. Amer. Math. Soc., to appear. | MR | Zbl

[QV2] F. Quirós - J.L. Vázquez, Asymptotic behaviour of the porous media, Hele-Shaw and Stefan equations in an exterior domain, in preparation.

[S4] A.A. Samarskii - V.A. Galaktionov - S.P. Kurdyumov - A.P. Mikhailov, "Blow-up in Problems for Quasilinear Parabolic Equations", Walter de Gruyter, Berlin, 1995. | MR | Zbl

[V1] J.L. Vázquez, Symétrisation pour ut = Δϕ (u) et applications, C. R. Acad. Sci. Paris 295 (1982), 71-74. | Zbl

[V2] J.L. Vázquez, An introduction to the mathematical theory of the porous medium equation, in "Shape Optimization and Free Boundaries" (M.C. Delfour, eds.) Mathematical and Physical Sciences, Series C, vol. 380, Kluwer Ac. Publ., Dordrecht, Boston and Leiden, 1992, pp. 347-389. | MR | Zbl

[VV] J.L. Vázquez - L. Véron, Different kinds of singular solutions of nonlinear parabolic equations, in "Nonlinear Problems in Applied Mathematics", volume in honor of Ivar Stakgold on his 70th birthday (T. S. Angell et al., eds.) SIAM, Philadelphia, 1996, pp. 240-249. | Zbl

[Z] W.P. Ziemer, Interior and boundary continuity of weak solutions of degenerate parabolic equations, Trans. Amer. Math. Soc. 271 n. 2 (1982), 733-748. | MR | Zbl