The Existence and Behavior of Solutions for Nonlocal Boundary Problems
1 Department of Mathematics, Shanghai University, Shanghai 200444, China
2 Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China
Boundary Value Problems 2009, 2009:484879 doi:10.1155/2009/484879Published: 31 March 2009
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.