Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 61439, 23 pages
doi:10.1155/JAMSA/2006/61439
Solution of a transmission problem for semilinear
parabolic-hyperbolic equations by the time-discretization
method
Department of Mathematics, The Larbi Ben M'hidi
University Centre, P.O. Box 565, Oum El-Bougui 04000, Algeria
Received 7 August 2004; Revised 7 May 2005; Accepted 24 May 2005
Copyright © 2006 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.
Abstract
We consider a transmission problem for semilinear
parabolic-hyperbolic equations. Existence, uniqueness, and
continuous dependence of the solution upon the data are proved by
using the time-discretization method. Besides, some convergence
results of the approximations are established.