**Lothar Jentsch and David Natroshvili**

## Three-dimensional Mathematical Problems of Thermoelasticity of Anisotropic Bodies

**abstract:**

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.