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