On Variational Methods of Investigation of Mathematical Problems for Thermoelastic Piezoelectric Solids

Abstract

In this paper we present the results of investigation of the boundary and initial-boundary value problems corresponding to mathematical models of thermoelastic piezoelectric solids with regard to magnetic field. We consider three-dimensional static and dynamic models of general inhomogeneous anisotropic thermoelastic piezoelectric solids with mixed boundary conditions, when on certain parts of the boundary density of surface force, and normal components of the electric displacement, magnetic induction, and heat flux are given, and on the remaining parts of the boundary mechanical displacement, temperature, electric and magnetic potentials vanish. We obtain variational formulations of the boundary and initial-boundary value problems in suitable function spaces and present the existence, uniqueness and continuous dependence results.