On Approximation of Lord-Shulman Model for Thermoelastic Plates with Variable Thickness by Two-Dimensional Problems

In the present paper thermoelastic solid is considered within the framework of Lord- Shulman non­classical theory of thermoelasticity. Applying variational approach initial­boundary value problem corresponding to the three-dimensional model is investigated in suitable spaces of vector-valued distributions with values in Sobolev spaces. An algorithm of approximation by two-dimensional problems of the three-dimensional dynamical model for plate with variable thickness is constructed, when densities of surface force and normal component of heat flux are given on the upper and the lower face surfaces of the plate. The obtained two-dimensional initial-boundary value problems are investigated in suitable function spaces. Moreover, convergence of the sequence of vector-functions of three space variables restored from the solutions of the constructed two-dimensional problems to the solution of the original three-dimensional initial-boundary value problem is proved and under additional conditions the rate of convergence is estimated. © 2014 Bull. Georg. Natl. Acad. Sci.