On a nonlinear generalized thermoelastic system with obstacle (Q664629)

The authors study the \(n\)-dimensional semilinear thermoelastic system with unilateral boundary conditions (Signorini's conditions), which describes the motion of an thermoelastic body in contact with a rigid obstacle without attrition. The authors first reformulate the original contact problem as a variational inequality problem and give an approximate variational problem by introducing a penalty term. Then, by careful energy estimates and the compactness argument, the authors prove the global existence of weak solutions. In the one-dimensional case, the authors are able to exploit the one-dimensional features, such as the better regularity under Signorini's boundary conditions, to show that the solutions decay exponentially as time goes to infinity.