Boundary Value Problems
Volume 2010 (2010), Article ID 681709, 15 pages
doi:10.1155/2010/681709
Research Article

The Jump Problem for Mixed-Type Equations with Defects on the Type Change Line

Ahmed Maher1,2

1Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt
2Department of Mathematics, The Teacher's College in Makkah, Umm Al-Qura University, P.O. Box 2064, Makkah, Saudi Arabia

Received 2 January 2010; Accepted 4 June 2010

Academic Editor: Zhitao Zhang

Copyright © 2010 Ahmed Maher. 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

The jump problem and problems with defects on the type change line for model mixed-type equations in the mixed domains are investigated. The explicit solutions of the jump problem are obtained by the method of integral equations and by the Fourier transformation method. The problems with defects are reduced to singular integral equations. Some results for the solution of the equation under consideration are discussed concerning the existence and uniqueness for the solution of the suggested problem.