DOUBLY NONLINEAR PARABOLIC EQUATIONS INVOLVING VARIABLE EXPONENTS

被引：6
|
作者：
Akagi, Goro [1 ]
机构：
[1] Kobe Univ, Grad Sch Syst Informat, Nada Ku, Kobe, Hyogo 6578501, Japan
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2014年 / 7卷 / 01期
关键词：
Doubly nonlinear; parabolic; variable exponent; p(x)-Laplacian; subdifferential; evolution equation; EVOLUTION-EQUATIONS; EXISTENCE; FUNCTIONALS; SPACES;
D O I：
10.3934/dcdss.2014.7.1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with doubly nonlinear parabolic equations involving variable exponents. The existence of solutions is proved by developing an abstract theory on doubly nonlinear evolution equations governed by gradient operators. In contrast to constant exponent cases, two nonlinear terms have inhomogeneous growth and some difficulty may occur in establishing energy estimates. Our method of proof relies on an efficient use of Legendre-Fenchel transforms of convex functionals and an energy method.
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页码：1 / 16
页数：16
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