A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation
Caffarelli, Luis A ; Roquejoffre, Jean-Michel
Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002), p. 41-80 / Harvested from Numdam
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@article{AIHPC_2002__19_1_41_0,
     author = {Caffarelli, Luis and Roquejoffre, Jean-Michel},
     title = {A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {19},
     year = {2002},
     pages = {41-80},
     mrnumber = {1902545},
     zbl = {1016.35038},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2002__19_1_41_0}
}

Caffarelli, Luis A; Roquejoffre, Jean-Michel. A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation. Annales de l'I.H.P. Analyse non linéaire, Tome 19 (2002) pp. 41-80. http://gdmltest.u-ga.fr/item/AIHPC_2002__19_1_41_0/

[1] Aronson D.G., Bénilan P., Régularité des solutions de l'équation des milieux poreux dans RN, C. R. Acad. Sci. Paris 288 (1979) 103-105. | MR 524760 | Zbl 0397.35034

[2] Aronson D.G., Caffarelli L.A., Kamin S., How an initially stationary interface begins to move in porous medium flow, SIAM J. Math. Anal. 14 (1983) 639-658. | MR 704481 | Zbl 0542.76119

[3] Atkinson F.V., Peletier L.A., Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971) 369-379. | MR 334666 | Zbl 0249.35043

[4] Atkinson F.V., Peletier L.A., Similarity solutions of the nonlinear diffusion equation, Arch. Rational Mech. Anal. 54 (1974) 373-392. | MR 344559 | Zbl 0293.35039

[5] Audounet J., Giovangigli V., Roquejoffre J.-M., A threshold phenomenon arising in the propagation of a spherical flame, Physica D 121 (1998) 295-316. | MR 1645427 | Zbl 0938.80003

[6] Caffarelli L.A., A Harnack inequality approach to the regularity of free boundaries. I. Lipschitz free boundaries are C1,α, Rev. Mat. Iberoamericana 3 (1987) 39-62. | Zbl 0676.35085

[7] Caffarelli L.A., Vazquez J.-L., Viscosity solutions for the porous medium equation, in: Differential Equations: La Pietra 1996 (Florence), Proc. Sympos. Pure Math., 65, American Mathematical Society, Providence, RI, 1999. | MR 1662747 | Zbl 0929.35072

[8] Caffarelli L.A., Vazquez J.-L., Wolanski N.I., Lipschitz continuity of solutions and interfaces in the N-dimensional porous medium equation, Indiana Univ. Math. J. 36 (1987) 373-401. | MR 891781 | Zbl 0644.35058

[9] Caffarelli L.A., Wolanski N.I., C1,α regularity of the free boundary for the N-dimensional porous media equation, Comm. Pure Appl. Math. 43 (1990) 885-902. | Zbl 0728.76103

[10] Clément P., Gripenberg G., Londen S.-O., Hölder regularity for a linear fractional evolution equation, in: Topics in Nonlinear Analysis, H. Amann Anniversary Volume, Birkhäuser, 1999, pp. 69-82. | MR 1725566 | Zbl 0920.35004

[11] Gorenflo R., Vessela S., Abel Integral Equations, Springer, New York, 1991. | MR 1095269 | Zbl 0717.45002

[12] Gordeev A.V., Grechikha A.V., Kalda Y.L., Rapid penetration of a magnetic field into a plasma along an electrode, Sov. J. Plasma Phys. 16 (1) (1990) 55-57.

[13] Gripenberg G., Londen S.-O., Fractional derivatives and smoothing in nonlinear conservation laws, Diff. Int. Eq. 8 (1995) 1961-1976. | MR 1348960 | Zbl 0885.45005

[14] Henry D., Geometric Theory of Semilinear Parabolic Equations, Springer, New York, 1981. | MR 610244 | Zbl 0456.35001

[15] Ladyzhenskaya O.A., Ural'Tceva N.N., Solonnikov V.A., Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, RI, 1968. | Zbl 0174.15403

[16] Méhats F., Thèse de doctorat de l'École polytechnique, 1997.

[17] Méhats F., Roquejoffre J.-M., A nonlinear oblique derivative problem for the heat equation, Part I: Basic results, Ann. Inst. Henri Poincaré, Analyse non linéaire 16 (1999) 221-253. | Numdam | MR 1674770 | Zbl 0922.35072

[18] Méhats F., Roquejoffre J.-M., A nonlinear oblique derivative problem for the Heat equation, Part II: Singular self-similar solutions, Ann. Inst. Henri Poincaré, Analyse non linéaire 16 (1999) 691-724. | Numdam | MR 1720513 | Zbl 0945.35047

[19] Walter W., Differential Inequlities, Springer, Berlin, 1964. | MR 172076