On a higher order two dimensional thermoelastic system combining a local and nonlocal boundary conditions

Due to their importance and numerous applications, evolution mixed problems with non local constraints in the boundary conditions have been extensively studied during the two last decades. In this paper, we consider an initial boundary value problem for a higher order thermoelastic system arising in linear thermoelasticity which combines some Dirichlet and weighted integral boundary conditions. The studied system modelizes in general a Kirchoff plate. We prove the well posedness of the given problem. Our proofs are mainly based on some a priori bounds in some Sobolev type space functions and on some density arguments