Local Boundedness of Weak Solutions for Nonlinear Parabolic Problem with p(x)-Growth

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.