Boundary Value Problems 
Volume 2007 (2007), Article ID 80929, 10 pages
doi:10.1155/2007/80929
Research Article

On Comparison Principles for Parabolic Equations with Nonlocal Boundary Conditions

Yuandi Wang1 and Hamdi Zorgati2,3

 1Department of Mathematics, Shanghai University, Shanghai 200444, China
2Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, Zürich CH-8057, Switzerland
3Department of Mathematics, Campus Universitaire, University of Tunis, Elmanar 2092, Tunisia
Received 5 December 2006; Revised 8 March 2007; Accepted 3 May 2007

Recommended by Peter Bates

Abstract

A generalization of the comparison principle for a semilinear and a quasilinear parabolic equations with nonlocal boundary conditions including changing sign kernels is obtained. This generalization uses a positivity result obtained here for a parabolic problem with nonlocal boundary conditions.