@article{AIHPC_2002__19_1_41_0, author = {Caffarelli, Luis A 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}, pages = {41--80}, publisher = {Elsevier}, volume = {19}, number = {1}, year = {2002}, mrnumber = {1902545}, zbl = {1016.35038}, language = {en}, url = {http://www.numdam.org/item/AIHPC_2002__19_1_41_0/} }
TY - JOUR AU - Caffarelli, Luis A AU - Roquejoffre, Jean-Michel TI - A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2002 SP - 41 EP - 80 VL - 19 IS - 1 PB - Elsevier UR - http://www.numdam.org/item/AIHPC_2002__19_1_41_0/ LA - en ID - AIHPC_2002__19_1_41_0 ER -
%0 Journal Article %A Caffarelli, Luis A %A Roquejoffre, Jean-Michel %T A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation %J Annales de l'I.H.P. Analyse non linéaire %D 2002 %P 41-80 %V 19 %N 1 %I Elsevier %U http://www.numdam.org/item/AIHPC_2002__19_1_41_0/ %G en %F 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, Volume 19 (2002) no. 1, pp. 41-80. http://www.numdam.org/item/AIHPC_2002__19_1_41_0/
[1] Régularité des solutions de l'équation des milieux poreux dans RN, C. R. Acad. Sci. Paris 288 (1979) 103-105. | MR | Zbl
, ,[2] How an initially stationary interface begins to move in porous medium flow, SIAM J. Math. Anal. 14 (1983) 639-658. | MR | Zbl
, , ,[3] Similarity profiles of flows through porous media, Arch. Rational Mech. Anal. 42 (1971) 369-379. | MR | Zbl
, ,[4] Similarity solutions of the nonlinear diffusion equation, Arch. Rational Mech. Anal. 54 (1974) 373-392. | MR | Zbl
, ,[5] A threshold phenomenon arising in the propagation of a spherical flame, Physica D 121 (1998) 295-316. | MR | Zbl
, , ,[6] 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
,[7] 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 | Zbl
, ,[8] Lipschitz continuity of solutions and interfaces in the N-dimensional porous medium equation, Indiana Univ. Math. J. 36 (1987) 373-401. | MR | Zbl
, , ,[9] C1,α regularity of the free boundary for the N-dimensional porous media equation, Comm. Pure Appl. Math. 43 (1990) 885-902. | Zbl
, ,[10] Hölder regularity for a linear fractional evolution equation, in: Topics in Nonlinear Analysis, H. Amann Anniversary Volume, Birkhäuser, 1999, pp. 69-82. | MR | Zbl
, , , , , Abel Integral Equations, Springer, New York, 1991. |[12] Rapid penetration of a magnetic field into a plasma along an electrode, Sov. J. Plasma Phys. 16 (1) (1990) 55-57.
, , ,[13] Fractional derivatives and smoothing in nonlinear conservation laws, Diff. Int. Eq. 8 (1995) 1961-1976. | MR | Zbl
, ,[14] Geometric Theory of Semilinear Parabolic Equations, Springer, New York, 1981. | MR | Zbl
,[15] Linear and Quasilinear Equations of Parabolic Type, American Mathematical Society, Providence, RI, 1968. | Zbl
, , ,[16] Méhats F., Thèse de doctorat de l'École polytechnique, 1997.
[17] 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 | Zbl
, ,[18] 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 | Zbl
, ,[19] Differential Inequlities, Springer, Berlin, 1964. | MR
,