具有双重变指数的非线性抛物方程组弱解的存在性

The existence of the weak solution of nonlinear parabolic equations with double variable exponents

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.