Singular Perturbations of Variational-Hemivariational Inequalities

Abstract

This paper is devoted to an analysis of singular perturbations of inequality problems. For a general variational-hemivariational inequality, it is shown rigorously that under appropriate conditions, as the singular perturbation parameter approaches zero, the solution of the singularly perturbed problem converges to the solution of the limiting problem. As corollaries of this general result, we have similar convergence results for singularly perturbed problems of “pure” hemivariational inequalities and of variational inequalities. The results are illustrated in the study of an obstacle plate bending problem.

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