Journal of Applied Mathematics and Stochastic Analysis
Volume 2005 (2005), Issue 1, Pages 13-28
Rothe time-discretization method for a nonlocal problem arising in thermoelasticity
Département de Mathématiques, Centre Universitaire Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria
Received 26 November 2003; Revised 21 July 2004
Copyright © 2005 Nabil Merazga and Abdelfatah Bouziani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We investigate a model parabolic mixed problem with purely boundary integral conditions arising in the context of thermoelasticity. Using the Rothe method which is based on a semidiscretization of the given problem with respect to the time variable, the questions of existence, uniqueness, and continuous dependence upon data of a weak solution are proved. Moreover, we establish convergence and derive an error estimate for a semidiscrete approximation.