Convergence results for elliptic quasivariational inequalities

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• 作者：Mircea Sofonea ; Ahlem Benraouda
• 关键词：Quasivariational inequality ; Penalty method ; Convergence result ; Elastic rod ; Nonlinear spring ; Unilateral constraint ; Weak solution
• 刊名：Zeitschrift für angewandte Mathematik und Physik
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：68
• 期：1
• 全文大小：
• 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
• 出版者：Springer International Publishing
• ISSN：1420-9039
• 卷排序：68

文摘

In this paper, we state and prove various convergence results for a general class of elliptic quasivariational inequalities with constraints. Thus, we prove the convergence of the solution of a class of penalized problems to the solution of the original inequality, as the penalty parameter converges to zero. We also prove a continuous dependence result of the solution with respect the convex set of constraints. Then, we consider a mathematical model which describes the equilibrium of an elastic rod attached to a nonlinear spring. We derive the variational formulation of the model which is in a form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the model, and then we state and prove two convergence results and provide their corresponding mechanical interpretation.