A class of optimal control problems for piezoelectric frictional contact models. (English) Zbl 1217.49008
Summary: 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 by 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 present results on existence and uniqueness of a weak solution of the model and, under additional assumptions, of 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.
MSC:
| 49J30 | Existence of optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |
| 49J52 | Nonsmooth analysis |
| 49N45 | Inverse problems in optimal control |
| 49J20 | Existence theories for optimal control problems involving partial differential equations |
Keywords:
piezoelectric material; static process; control problem; bilateral contact; friction; hemivariational inequality; inverse problem; Clarke’s subdifferential; pseudomonotone operator; weak solutionReferences:
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