Mathematical analysis of static and dynamic three-dimensional models of thermo-electro-magneto-elastic solids

Abstract

This paper is devoted to the investigation of three-dimensional models of thermo-electro-magneto-elastic solids made of a multidomain inhomogeneous anisotropic material. General boundary and initial boundary value problems corresponding to the static and dynamic models are studied where, on certain parts of the boundary, mechanical displacement, electric and magnetic potentials and temperature vanish and, on the corresponding remaining parts of the boundary, the mechanical stress vector and components of the electric displacement, magnetic induction and heat flux along the outward normal vector of the boundary are given. Variational formulations of the boundary and initial boundary value problems are obtained and, applying them, existence and uniqueness results and the continuous dependence of solutions on given data, in suitable factor spaces of Sobolev spaces or spaces of vector-valued distributions, are proved.