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Existence of global weak solutions for coupled thermoelasticity with Barber`s heat exchange condition

Bień M.

Journal of Applied Analysis

2003

Vol. 9, nr 2

163-185

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, monotonic-ity and compactness methods. Some a priori bounds obtained with Gronwalls inequality in connection with the embedding and trace theorems lead to accomplishing a generalization of our previous study [5]. 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 Andrews et al. [3] and Elliot et al. [12].