Lothar Jentsch and David Natroshvili

Three-dimensional Mathematical Problems of Thermoelasticity of Anisotropic Bodies

Singular boundary value problems are considered for high order nonlinear equations in the case where the right-hand side may have singularities both in independent and phase variables. Existence, uniqueness theorems are proved. A priori asymptotic estimates of solutions are obtained. The obtained problems, in the case of the second order, involve those arising while studying the flow of a viscuous fluid when written in the so-called Crocco variables.

Mathematics Subject Classification: 31B10, 31B15, 35C15, 35E05, 35J55, 45F15, 73B30, 73B40, 73C15, 73C35, 73D30, 73K20.

Key words and phrases: Thermoelasticity, anisotripic bodies, thermoelastic vibrations, pseudo-oscillations, potential theory, pseudodifferential equations on manifold, fundamental solutions, radiation conditions, boundary value problems, interface problems, crack problems.