Vanishing viscosity for hemivariational inequalities modeling dynamic problems in elasticity

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• 作者：Stanisł ; aw Migó ; rski ; Anna Ochal
• 关键词：Hemivariational inequality ; Subdifferential ; Elasticity ; Evolution inclusion ; Parabolic regularization
• 刊名：Nonlinear Analysis
• 出版年：2007
• 出版时间：15 April 2007
• 年：2007
• 卷：66
• 期：8
• 页码：1840-1852
• 全文大小：231 K

文摘

In this paper we consider a mathematical model describing a dynamic linear elastic contact problem with nonmonotone skin effects. The subdifferential multivalued and multidimensional reaction–displacement law is employed. We treat an evolution hemivariational inequality of hyperbolic type which is a weak formulation of this mechanical problem. We establish a result on the existence of solutions to the Cauchy problem for the hemivariational inequality. This result is a consequence of an existence theorem for second order evolution inclusion. For the latter, using the parabolic regularization method, we obtain the solution as a limit when the viscosity term tends to zero.