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Open Access Research Article

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

Ahmed Maher

Author Affiliations

Department of Mathematics, Faculty of Science, Assiut University, Assiut 71516, Egypt

Department of Mathematics, The Teacher's College in Makkah, Umm Al-Qura University, P.O. Box 2064, Makkah, Saudi Arabia

Boundary Value Problems 2010, 2010:681709  doi:10.1155/2010/681709

Published: 27 June 2010

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.