Parabolic equations with double variable nonlinearities

Abstract

The paper is devoted to the study of the homogeneous Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions: ut = div ( a(x, t, u)|u|α(x,t)|∇u|p(x,t)−2∇u)+ f (x, t) with given variable exponents α(x, t) and p(x, t). We establish conditions on the data which guarantee the existence of bounded weak solutions in… (More)
DOI: 10.1016/j.matcom.2010.12.015

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