Home Existence of Global Weak Solutions for Coupled Thermoelasticity with Barber's Heat Exchange Condition
Article
Licensed
Unlicensed Requires Authentication

Existence of Global Weak Solutions for Coupled Thermoelasticity with Barber's Heat Exchange Condition

  • M. Bień
Published/Copyright: June 9, 2010

Abstract

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 Gronwalls inequality in connection with the embedding and trace theorems lead to accomplishing a generalization of our previous study [Bień, Math. Methods Appl. Sci. 19: 1265–1277, 1996]. 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. [Shi, Shillor, Wright, Appl. Math. Optim. 28: 11–48, 1993] and Elliot et al. [Tang, Nonlinear Anal. 23: 883–898, 1994].


The correspondence address: Al. Smigłego-Rydza 52 m. 20, 93-281 Łódź, Poland

Received: 1998-05-29
Revised: 2002-07-17
Published Online: 2010-06-09
Published in Print: 2003-December

© Heldermann Verlag

Downloaded on 22.10.2025 from https://www.degruyterbrill.com/document/doi/10.1515/JAA.2003.163/html
Scroll to top button