摘要
研究下列带有双重变指数的非线性抛物方程组在第一初边值条件下弱解的存在性:{ut-div(|u|α(x,t)|▽u|p(x,t)-2▽u)=f(x,t,u,v) vt-div(|v|β(x,t)|▽v|q(x,t)-2▽v)=g(x,t,u,v)}在适当的Sobolev-Orlicz空间里,利用抛物正则化和Galerkin逼近方法,建立了保证有界弱解存在的充分条件.
The aim of the paper is to investigate the existence of weak solution of the following nonlinear parabolic equations with double variable exponents under the first initial boundary value conditions :
{ut-div(|u|^α(x,t)|△u|^p(x,t)-2△u)=f(x,t,u,v)
vt-div(|u|^β(x,t)|△v|^q(x,t)-2△v)=g(x,t,u,v)
By using the methods of parabolic regularization and Galerkin' s approximations, the authors establish the sufficient conditions which guarantee the existence of bounded weak solutions in suitable Sobolev - Odicz spaces.
出处
《福州大学学报(自然科学版)》
CAS
CSCD
北大核心
2014年第1期1-7,共7页
Journal of Fuzhou University(Natural Science Edition)
基金
国家自然科学基金资助项目(11301083)
关键词
非线性抛物方程组
双重变指数
非标准增长条件
存在性
nonlinear parabolic system
double variable exponents
nonstandard growth conditions
existence