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

On a mixed nonlinear one point boundary value problem for an integrodifferential equation

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.