A PARABOLIC-SYSTEM MODELING THE THERMOELASTIC CONTACT OF 2 RODS

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