Electron. J. Diff. Equ., Vol. 2015 (2015), No. 172, pp. 1-23.

Existence and boundedness of solutions for evolution variational inequalities with p(x,t)-growth

Mingqi Xiang, Yongqiang Fu, Binlin Zhang

In this article, we study a class of evolution variational inequalities with p(x,t)-growth conditions on bounded domains. By means of the penalty method and Galerkin's approximation, we obtain the existence of weak solutions. Moreover, the boundedness of weak solutions is also investigated by applying Moser's iterative method.

Submitted March 9, 2015. Published June 22, 2015.
Math Subject Classifications: 35K86, 35R35, 35D30.
Key Words: Evolution variational inequality; variable exponent space; penalty method.

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Mingqi Xiang
College of Science
Civil Aviation University of China
Tianjin 300300, China
email: xiangmingqi_hit@163.com
Yongqiang Fu
Department of Mathematics
Harbin Institute of Technology
Harbin 150001, China
email: fuyongqiang@hit.edu.cn
Binlin Zhang
Department of Mathematics
Heilongjiang Institute of Technology
Harbin 150050, China
email: zhangbinlin2012@163.com

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