Copyright © 2010 Yongqiang Fu and Ning Pan. 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

We study the nonlinear parabolic problem with p(x)-growth conditions in the space W1,xLp(x)(Q) and give a local boundedness theorem of weak solutions for the following equation (∂u/∂t)+A(u)=0, where A(u)=−diva(x,t,u,∇u)+a0(x,t,u,∇u),a(x,t,u,∇u) and a0(x,t,u,∇u) satisfy p(x)-growth conditions with respect to u and ∇u.