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Journal of Applied Analysis 9 (2003), No. 2, 163--186
Copyright Heldermann Verlag 2003
Existence of Global Weak Solutions for Coupled Thermoelasticity with Barber’s Heat Exchange
Condition
Marian Bien
LZG Leczyca S.A., R&D Department, Kopalniana 9, Leczyca, Poland
The existence of global weak solutions for coupled thermoelasticity with the
nonlinear contact boundary condition and Barber's heat exchange condition is proved
via the Faedo-Galerkin, monotonicity and compactness methods. Some a priori bounds
obtained with Gronwall’s inequality in connection with the embedding and trace theorems
lead to accomplishing a generalization of a previous study [Math. Methods Appl. Sci.
19 (1996) 1265--1277]. The heat-exchange coefficient associated with Barber's heat
exchange condition is dependent only on the normal displacement. This dependence is
described by a bounded Lipschitz function. Moreover, this study is some extension of
works due to K. T. Andrews, P. Shi, M. Shillor and S. Wright [Appl. Math. Optim. 28
(1993) 11--48] and C. M. Elliot and Q. I. Tang [Nonlinear Anal. 23 (1994) 883--898].
Keywords: Coupled thermoelasticity, Barber's heat exchange condition, thermoelastic
contact, existence of global weak solutions to the initial boundary value problem.
MSC 2000: 35B45, 35K05, 35L55, 35Q72, 73C35, 73B30, 73C35.
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