Boundary Value Problems 
Volume 2008 (2008), Article ID 814947, 8 pages
doi:10.1155/2008/814947
Research Article

On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation

Said Mesloub

 Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
Received 31 August 2007; Accepted 5 February 2008

Recommended by Martin Schechter

Abstract

This paper is devoted to the study of a mixed problem for a nonlinear parabolic integro-differential equation which mainly arise from a one dimensional quasistatic contact problem. We prove the existence and uniqueness of solutions in a weighted Sobolev space. Proofs are based on some a priori estimates and on the Schauder fixed point theorem. we also give a result which helps to establish the regularity of a solution.