Open Access Research Article

The Existence and Behavior of Solutions for Nonlocal Boundary Problems

Yuandi Wang1* and Shengzhou Zheng2

Author Affiliations

1 Department of Mathematics, Shanghai University, Shanghai 200444, China

2 Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

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Boundary Value Problems 2009, 2009:484879  doi:10.1155/2009/484879

Published: 31 March 2009

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.