Archive for Rational Mechanics and Analysis

, Volume 153, Issue 1, pp 1–37

Unique Global Solvability for¶Initial-Boundary Value Problems¶in One-Dimensional Nonlinear Thermoviscoelasticity

Authors

  • Stephen J. Watson
    • Department of Mathematics¶Louisiana State University¶Baton Rouge, LA 70803¶e-mail: watson@math.lsu.edu

DOI: 10.1007/s002050050007

Cite this article as:
Watson, S. Arch. Rational Mech. Anal. (2000) 153: 1. doi:10.1007/s002050050007
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Abstract:

The balance laws of mass, momentum and energy are considered for a broad class of one-dimensional nonlinear thermoviscoelastic materials. For the initial-boundary value problem corresponding to pinned endpoints held at constant temperature, we establish existence and uniqueness of temporally global classical solutions for initial data of unrestricted size. Our approach also applies to all boundary conditions involving pinned or stress-free endpoints which are either held at constant temperature or insulated. An additional and novel feature of the theory is that solid-like and gaseous materials are treated in a unified way.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000