An initial boundary value problem for modeling a piezoelectric dipolar body. (English) Zbl 1392.74040
Summary: This study deals with the first initial boundary value problem in elasticity of piezoelectric dipolar bodies. We consider the most general case of an anisotropic and inhomogeneous elastic body having a dipolar structure. For two different types of restrictions imposed on the problem data, we prove two results regarding the uniqueness of solution, by using a different but accessible method. Then, the mixed problem is transformed in a temporally evolutionary equation on a Hilbert space, conveniently constructed based on the problem data. With the help of a known result from the theory of semigroups of operators, the existence and uniqueness of the weak solution for this equation are proved.
MSC:
| 74F15 | Electromagnetic effects in solid mechanics |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
Keywords:
piezoelectricity; uniqueness; evolutionary equation; weak solution; existence; semigroup of operatorsReferences:
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