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

Abdelfatah Bouziani

 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

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.