Coupled dynamic thermoviscoelasticity problem

We construct a closed analytic solution of a coupled dynamic thermoviscoelasticity problem for bodies of canonical shape. The solution is represented in the form of spectral expansions in a biorthogonal eigenfunction system of the nonself-adjoint pencil of differential operators generated by the problem under study. The spectral expansions are obtained with the help of a special class of nonsymmetric integral transforms.