Article ID Journal Published Year Pages File Type
4619203 Journal of Mathematical Analysis and Applications 2010 14 Pages PDF
Abstract

In this paper, we study the existence of solutions for nonlinear parabolic initial boundary value problem with p(x)p(x)-growth conditions in the space W1,xLp(x)(Q)∩L∞(0,T;L2(Ω))W1,xLp(x)(Q)∩L∞(0,T;L2(Ω)), and give an existence theorem of weak solutions for the following equation∂u∂t+A(u)=f, where A(u)=−diva(x,t,u,∇u)+a0(x,t,u,∇u), a(x,t,u,∇u)a(x,t,u,∇u) and a0(x,t,u,∇u)a0(x,t,u,∇u) satisfy p(x)p(x)-growth conditions with respect to u and ∇u  , and f∈W−1,xLq(x)(Q)f∈W−1,xLq(x)(Q).

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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