On a coupled nonlinear singular thermoelastic system

For a coupled nonlinear singular system of thermoelasticity with one space dimension, we consider its initial boundary value problem on an interval. For one of the unknowns a classical condition is replaced by a nonlocal constraint of integral type. Because of the presence of a memory term in one of the equations and the presence of a weighted boundary integral condition, the solution requires a delicate set of techniques. We first solve a particular case of the given nonlinear problem by using a functional analysis approach. On the basis of the results obtained and an iteration method we establish the well-posedness of solutions in weighted Sobolev spaces.