A class of optimal control problems for piezoelectric frictional contact models

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• 作者：Zdzis&#x142 ; aw Denkowski^a ; ^{denkowski@ii.uj.edu.pl} ; Stanis&#x142 ; aw Migó ; rski ; ^a ; ^{migorski@ii.uj.edu.pl} ; Anna Ochal^a ; ^{ochal@ii.uj.edu.pl}
• 关键词：Piezoelectric material ; Static process ; Control problem ; Bilateral contact ; Friction ; Hemivariational inequality ; Inverse problem ; Clarke subdifferential ; Pseudomonotone operator ; Weak solution
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2011
• 出版时间：June 2011
• 年：2011
• 卷：12
• 期：3
• 页码：1883-1895
• 全文大小：305 K

文摘

We consider control problems for a mathematical model describing the frictional bilateral contact between a piezoelectric body and a foundation. The material’s behavior is modeled with a linear electro–elastic constitutive law, the process is static and the foundation is assumed to be electrically conductive. Both the friction and the electrical conductivity conditions on the contact surface are described with the Clarke subdifferential boundary conditions. The weak formulation of the problem consists of a system of two hemivariational inequalities. We provide the results on existence and uniqueness of a weak solution to the model and, under additional assumptions, the continuous dependence of a solution on the data. Finally, for a class of optimal control problems and inverse problems, we prove the existence of optimal solutions.