On the theory of heat conduction in micromorphic continua

The paper is concerned with the linear theory of heat conduction in micromorphic continua. First, a study of boundary-value problems of the stationary theory is presented. A representation of Galerkin type is established and fundamental solutions are derived. The potentials of single layer and double layer are used to reduce the boundary-value problems to singular integral equations. Existence and uniqueness results are established. The second part of the paper is devoted to non-stationary thermal fields. A continuous dependence result and an existence theorem are presented.