Recherche et téléchargement d’archives de revues mathématiques numérisées

 
 
  Table des matières de ce fascicule | Article précédent | Article suivant
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'institut Henri Poincaré (C) Analyse non linéaire, 19 no. 1 (2002), p. 41-80
Texte intégral djvu | pdf | Analyses MR 1902545 | Zbl 1016.35038 | 1 citation dans Numdam

URL stable: http://www.numdam.org/item?id=AIHPC_2002__19_1_41_0

Bibliographie

[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
Copyright Cellule MathDoc 2014 | Crédit | Plan du site