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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006, Article ID 61439, 23 pages
http://dx.doi.org/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.