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

Melnik (R.)V.N.

Continuous Media Dynamics, 99, 60-73, 1990


In this paper, we analyse the two-dimensional mathematical model of a nonstationary process in an electroelastic medium. We focus on a situation where the mechanical stress-strain and electromagnetic fields are coupled. The generalized solution of the governing initial-boundary value problems is defined in the appropriate Sobolev spaces. The proof of the existence and uniqueness of this solution is based on the construction of approximate solutions by means of the Faedo-Galerkin method. Since the method of proof is constructive, it also provides a way for the construction of efficient numerical approximations for such problems.