(1) Fakultät für Mathematik, Technische Universität Chemnitz-Zwickau, Reichenhainer Str. 41, D-09107 Chemnitz, Germany;(2) Department of Mathematics, Georgian Technical University, Kostava str. 77, 380075 Tbilisi, Georgia
Abstract:
Three-dimensional mathematical problems of the interaction between thermoelastic and scalar oscillation fields in a general physically anisotropic case are studied by the boundary integral equation methods. Uniqueness and existence theorems are proved by the reduction of the original interface problems to equivalent systems of boundary pseudodifferential equations. In the non-resonance case the invertibility of the corresponding matrix pseudodifferential operators in appropriate functional spaces is shown on the basis of the generalized Sommerfeld-Kupradze type thermoradiation conditions for anisotropic bodies. In the resonance case the co-kernels of the pseudodifferential operators are analysed and the efficient conditions of solvability of the original interface problems are established.