The asymptotic separation of variables in thermoelastic problem for anisotropic layer with inhomogeneous boundary conditions

A method for resolving a thermoelasticity problem with inhomogeneous boundary conditions is presented. Boundary conditions represent uneven surface heating of the layer. An asymptotic procedure for separation of variables based on introduction of additional dimensional scales is used. With an additional assumption that the unevenness of the heating is small enough this procedure makes it possible to obtain the solution. The method is shown for periodic heating case. After the separation of variables the solution is obtained using Fourier series.