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.
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.