Nonlinear parabolic problems in Musielak-Orlicz spaces

被引：41

作者：

Swierczewska-Gwiazda, Agnieszka ^{[1
]}

机构：

[1] Univ Warsaw, Inst Appl Math & Mech, PL-02097 Warsaw, Poland

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 98卷

关键词：

Musielak-Orlicz spaces; Modular convergence; Nonlinear parabolic inclusion; Maximal monotone graph; EXISTENCE; EQUATIONS; THEOREM; FLUIDS; FLOWS; OPERATORS; MODEL;

D O I：

10.1016/j.na.2013.11.026

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Our studies are directed to the existence of weak solutions to a parabolic problem containing a multi-valued term. The problem is formulated in the language of maximal monotone graphs. We assume that the growth and coercivity conditions of a nonlinear term are prescribed by means of a time and space dependent N-function. This results in the formulation of the problem in generalized Musielak-Orlicz spaces. We are using density arguments, hence an important step of the proof is a uniform boundedness of appropriate convolution operators in Musielak-Orlicz spaces. For this purpose we shall need to assume a kind of logarithmic Holder regularity with respect to t and x. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：48 / 65

页数：18

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