A parabolic system modeling the thermoelastic contact of two rods

Abstract

We consider an initial-boundary value problem for a nonlinear parabolic system that arises naturally in modeling behavior of two (possibly dissimilar) thin homogeneous rods. Each rod is held fixed at one end and is free to expand or contract at the other, as a result of the evolution of its temperature and stress fields. The two rods may also come into contact at their free ends. We establish the existence and uniqueness of a strong solution to the system, assuming that the thermal expansion coefficients are small. The proofs rely on a priori estimates, the functional method of Ladyzhenskaya, and Schauder’s fixed-point theorem.