Uniqueness and existence for anisotropic degenerate parabolic equations with boundary conditions on a bounded rectangle

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Kobayasi, Kazuo¹  Ohwa, Hiroki² 

[1] Waseda Univ, Dept Math, Sch Educ, Shinjuku Ku, Tokyo 1698050, Japan

[2] Waseda Univ, Grad Sch Educ, Shinjuku Ku, Tokyo 1698050, Japan

关键词: Degenerate parabolic equation;    Anisotropic;    Dirichlet boundary problem;    Kinetic formulation;    Comparison theorem;    Uniqueness and existence;   

DOI  :  10.1016/j.jde.2011.09.008

来源: Elsevier

【 摘 要 】

We study the comparison principle for anisotropic degenerate parabolic-hyperbolic equations with initial and nonhomogeneous boundary conditions. We prove a comparison theorem for any entropy sub- and super-solution, which immediately deduces the L(1) contractivity and therefore, uniqueness of entropy solutions. The method used here is based upon the kinetic formulation and the kinetic techniques developed by Lions, Perthame and Tadmor. By adapting and modifying those methods to the case of Dirichlet boundary problems for degenerate parabolic equations we can establish a comparison property. Moreover, in the quasi-isotropic case the existence of entropy solutions is proved. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free