A parabolic system modeling the thermoelastic contact of two rods

Authors:
Kevin T. Andrews, Peter Shi, Meir Shillor and Steve Wright

Journal:
Quart. Appl. Math. **53** (1995), 53-68

MSC:
Primary 73B30; Secondary 35K60, 35Q72, 73T05

DOI:
https://doi.org/10.1090/qam/1315447

MathSciNet review:
MR1315447

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

DOI:
https://doi.org/10.1090/qam/1315447

Article copyright:
© Copyright 1995
American Mathematical Society