Journal of Applied Mathematics and Stochastic Analysis 
Volume 2005 (2005), Issue 1, Pages 13-28
doi:10.1155/JAMSA.2005.13

Rothe time-discretization method for a nonlocal problem arising in thermoelasticity

Nabil Merazga and Abdelfatah Bouziani

 Département de Mathématiques, Centre Universitaire Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria
Received 26 November 2003; Revised 21 July 2004

Abstract

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.