On the theory of dynamic thermoelasticity : PMM, vol. 42, no. 6, 1978, pp. 1093–1098

Use of the causality principle as radiation condition in dynamical problems of thermoelasticity is proposed. It follows from an analysis of the fundamental mathematical models describing the thermoelastic behavior of a continuous medium and used in the solution of specific problems, that some will yield physically unrealizable solutions. To eliminate the ambiguity in the solution which occurs, an approach is possible which has an explicit physical meaning and is based on the causality principle 1, 2]; it is required that the time source not yield a response earlier than the time of starting up of the source. Different kinds of radiation conditions of the Sommerfeld type are known in thermoelasticity problems 3 – 6].

To extract the unique solution in dynamical thermoelasticity problems, it is proposed in this paper to use the causality principle, which is equivalent to the requirement of analyticity of the solution in the upper half of the complex frequency plane; there are studied the analytic properties of the solutions of the fundamental boundary value problems for the models used most often for thermoelastic media, and there are made deductions about their physical realizability.