Weak Solutions to a Parabolic Problem Modeling Axially Symmetrical Thermoelastic Contact

Abstract

We consider a nonlinear parabolic problem that models the axially symmetric, quasistatic, mechanical behavior of a homogeneous hollow cylinder that may come into contact with a rigid obstacle. The problem has a nonlinear and nonlocal boundary condition that contains a pressure-dependent heat exchange coefficient. We model this coefficient both as a single-valued continuous function and as a measurable selection from a maximal monotone graph. In both instances we prove existence, regularity, and periodicity assertions for weak formulations of the problem, under the assumption that the thermal expansion coefficient is small.