THERMOELASTIC CONTACT WITH BARBER HEAT-EXCHANGE CONDITION

We consider a nonlinear parabolic problem that models the evolution of a one-dimensional thermoelastic system that may come into contact wit h a rigid obstacle. The mathematical problem is reduced to solving a n onlocal heat equation with a nonlinear and nonlocal boundary condition . This boundary condition contains a heat-exchange coefficient that de pends on the pressure when there is contact with the obstacle and on t he size of the gap when there is no contact. We model the heat-exchang e coefficient as both a single-valued function and as a measurable sel ection from a maximal monotone graph. Both of these models represent m odified versions of so-called imperfect contact conditions found in th e work of Barber. We show that strong solutions exist when the coeffic ient is taken to be a continuously differentiable function and that we ak solutions exist when the coefficient is taken to be a measurable se lection from a maximal monotone graph. The proofs of these results rev eal an interesting interplay between the regularity of the initial con dition and the behavior of the coefficient at infinity.