Existence of solutions for nonlinear parabolic problem with p(x)-growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:362

Article

Fu, Yongqiang¹  Pan, Ning¹ 

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

关键词: Nonlinear parabolic problem;    (WLp(x))-L-1,x(Q) space;    p(x)-Growth condition;   

DOI  :  10.1016/j.jmaa.2009.08.038

来源: Elsevier

【 摘 要 】

In this paper, we study the existence of solutions for nonlinear parabolic initial boundary value problem with p(x)-growth conditions in the space (WLp(x))-L-1,x(Q) boolean AND L-infinity (0, T; L-2(Omega)), and give an existence theorem of weak solutions for the following equation partial derivative u/partial derivative t + A(u) = f, where A(u) = -diva(x, t, u, del u) + a(0)(x, t, u, del u), a(x, t, u, del u) and a(0)(x, t, u, del u) satisfy p(x)-growth conditions with respect to u and del u, and f is an element of (W-1,xLq(x))(Q). (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free