Existence and Uniqueness of Generalized Solutions in Coupled Nonstationary Problems of Two Dimensional Electroelasticity

Melnik (R.)V.N.

Computational and Applied Mathematics Problems, 88, 123-134, 1990


Existence and uniqueness of solutions to static problems of electroelasticity have been studied by many authors. Of particular interest is the study of mathematical models and the development of numerical methods for their solution for coupled nonstationary problems of the theory of electroelasticity, in view of both their various technical applications and the mathematical complexity of the content of such problems. In earlier work, we described difference schemes for solving nonstationary problems of coupled electroelasticity for hollow infinite (the one-dimensional case) and finite (the two-dimensional model) piezoceramic cylinders, and carried out computational experiments. Here we analyze Galerkin approximations for the above-mentioned problems and, using the Faedo-Galerkin method, we prove an existence and uniqueness theorem for the generalized solutions of the mathematical models considered.