On uniqueness and existence of entropy solutions for a nonlinear parabolic problem with absorption期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On uniqueness and existence of entropy solutions for a nonlinear parabolic problem with absorption

Authors:	Boris Andreianov Karima Sbihi Petra Wittbold

Institution:	1. Laboratoire de Mathématiques de Besan?on, Université de Franche-Comté, 16 route de Gray, 25030, Besan?on Cedex, France 2. Technische Universit?t Berlin, Institut für Mathematik, Straβe des 17. Juni 136, D-10623, Berlin, Germany

Abstract:	The aim of this paper is to study, for L ¹-data, the absorption problem of parabolic type : $u_t - {\rm div} a(u, Du) + \beta(x, u) \ni f$ with Dirichlet boundary conditions and initial conditions. Here a satisfies the classical Leray-Lions hypotheses and β(x, ·) is the subdifferential ∂j(x, ·), where j is a convex function such that j(·, 0) = 0. Existence and uniqueness of an entropy solution is established.

Keywords:	Mathematics subject classification 2000:" target="_blank">Mathematics subject classification 2000: 35K55 31C15 35B20 47H06
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