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September  2008, 3(3): 675-689. doi: 10.3934/nhm.2008.3.675

Homogenization problem for a parabolic variational inequality with constraints on subsets situated on the boundary of the domain

T. A. Shaposhnikova 1, and  M. N. Zubova 2,

1. 

Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russian Federation
2. 

Department of Pure and Applied Mathematics, Russian Open State Technical University of Railway Transport, Moscow, Russian Federation

Received  April 2008 Published  June 2008

This paper is aimed at a homogenization problem for a parabolic variational inequality with unilateral constraints. The constraints on solutions are imposed on disk-shaped subsets belonging to the boundary of the domain and forming a periodic structure, so that one has a problem with rapidly oscillating boundary conditions on a part of the boundary. Under certain conditions on the relation between the period of the structure and the radius of the disks, the homogenized problem is obtained. With the help of special auxiliary functions, the solutions of the original variational inequalities are shown to converge to the solution of the homogenized problem in Sobolev space as the period of the structure tends to zero.
Keywords: variational inequalities, Homogenization, one-sided constraints.
Mathematics Subject Classification: Primary: 35B27, 35K8.
Citation: T. A. Shaposhnikova, M. N. Zubova. Homogenization problem for a parabolic variational inequality with constraints on subsets situated on the boundary of the domain. Networks & Heterogeneous Media, 2008, 3 (3) : 675-689. doi: 10.3934/nhm.2008.3.675
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