A nonlinear oblique derivative boundary value problem for the heat equation. Part 2 : singular self-similar solutions
Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) no. 6, pp. 691-724.
@article{AIHPC_1999__16_6_691_0,
     author = {Mehats, Florian and Roquejoffre, Jean-Michel},
     title = {A nonlinear oblique derivative boundary value problem for the heat equation. {Part} 2 : singular self-similar solutions},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {691--724},
     publisher = {Gauthier-Villars},
     volume = {16},
     number = {6},
     year = {1999},
     mrnumber = {1720513},
     zbl = {0945.35047},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1999__16_6_691_0/}
}
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Mehats, Florian; Roquejoffre, Jean-Michel. A nonlinear oblique derivative boundary value problem for the heat equation. Part 2 : singular self-similar solutions. Annales de l'I.H.P. Analyse non linéaire, Tome 16 (1999) no. 6, pp. 691-724. http://www.numdam.org/item/AIHPC_1999__16_6_691_0/

[1] R. Adams, Sobolev spaces, Acad. Press, 1975. | MR | Zbl

[2] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I and II, Comm. Pure Appl. Math., 12, 1959, pp. 623-727; 17, 1964, pp. 35-92. | MR | Zbl

[3] G. Barles, Fully nonlinear Neumann type boundary conditions for second-order elliptic and parabolic equations. J. Diff. Equations, Vol. 106, No. 1, 1993, pp. 90-106.. | MR | Zbl

[4] A. Chuvatin, Thèse de doctorat de l'École polytechnique, 1994.

[5] M.G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order Partial differential equations. Bull. Amer. Soc,. 27, 1992, pp. 1-67. | MR | Zbl

[6] L.C. Evans and R. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Math., CRC Press, Ann Arbor, 1992. | MR | Zbl

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

[8] R.J. Leveque, Numerical Methods for Conservation Laws, Lectures in Mathematics, Birkhäuser Verlag, 1990. | MR | Zbl

[9] G. Lieberman and N. Trudinger, Nonlinear oblique boundary value problems for nonlinear elliptic equations, Trans. A.M.S, Vol. 295, 1986, pp. 509-546. | MR | Zbl

[10] P.-L. Lions and P.E. Souganidis, Convergence of MUSCL type methods for scalar conservation laws, C.R. Acad. Sci. Paris, Vol. 311, 1990, Série I, pp. 259-264. | MR | Zbl

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

[12] F. Méhats and J.-M. Roquejoffre, A nonlinear oblique derivative boundary value problem for the heat equation. Part 1: Basic results, to appear in Ann. IHP,Analyse Non Linéaire. | Numdam | Zbl