Boundary Value Problems
Volume 2009 (2009), Article ID 484879, 17 pages
doi:10.1155/2009/484879
Research Article

The Existence and Behavior of Solutions for Nonlocal Boundary Problems

Yuandi Wang1 and Shengzhou Zheng2

1Department of Mathematics, Shanghai University, Shanghai 200444, China
2Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

Received 16 October 2008; Revised 19 March 2009; Accepted 23 March 2009

Academic Editor: Pavel Drabek

Copyright © 2009 Yuandi Wang and Shengzhou Zheng. 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.

Abstract

The purpose of this work is to investigate the uniqueness and existence of local solutions for the boundary value problem of a quasilinear parabolic equation. The result is obtained via the abstract theory of maximal regularity. Applications are given to some model problems in nonstationary radiative heat transfer and reaction-diffusion equation with nonlocal boundary flux conditions.