Dumina O. Potential theory methods in dynamic problems for thermoelastic media

The object of study: thermoelasticity. The aim of study: to prove the unique solvability of the boundary pseudodifferential equation systems that appear when one represents the solutions of the initial thermoelastic problems by different combinations of the retarded single and double layer potentials. Methods: variational, potentila theory, integral transformations, theory of partial differential equations, theory of functions of complex variable. Theoretical and practical results: For the first time the unique solvability in the one-parameter scale of Sobolev spaces was proved for the boundary equation system that appear when one represents the solutions of the two main dynamic problems for themoelastic media, the problems with mixed boundary conditions, the problems of transient diffraction of thermoelastic waves on unclosed surface and the dynamic contact problem by different combinations of retarded single and double layer potentials. It is shown that the surface potentials with densities that satisfy mentioned above systems are the solutions of the corresponding problems for the thermoelasticity set of equation. The sphere of application: mathematical physics.