Mingqi Xiang, Yongqiang Fu
Abstract:
In this article, we study a class of nonlocal quasilinear parabolic
variational inequality involving p(x)-Laplacian operator and gradient
constraint on a bounded domain. Choosing a special penalty functional
according to the gradient constraint, we transform the variational
inequality to a parabolic equation. By means of Galerkin's approximation
method, we obtain the existence of weak solutions for this equation,
and then through a priori estimates, we obtain the weak solutions of
variational inequality.
Submitted March 7, 2013. Published April 19, 2013.
Math Subject Classifications: 35K30, 35K86, 35K59.
Key Words: Nonlocal evolution variational inequality; variable exponent space;
Galerkin approximation; penalty method.
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Mingqi Xiang Department of Mathematics, Harbin Institute of Technology Harbin, 150001, China email: xiangmingqi_hit@163.com | |
Yongqiang Fu Department of Mathematics, Harbin Institute of Technology Harbin, 150001, China email: fuyqhagd@yahoo.cn |
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