Boundary Value Problems
Volume 2008 (2008), Article ID 814947, 8 pages
On a Mixed Nonlinear One Point Boundary Value Problem for an Integrodifferential Equation
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
Academic Editor: Martin Schechter
Copyright © 2008 Said Mesloub. 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.
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.