Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 100, pp. 117.
Weak solutions for nonlocal evolution variational inequalities
involving gradient constraints and variable exponent
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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