Parabolic equations with double variable nonlinearities

S. Antontsev and S. Shmarev

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 81, issue 10, 2018-2032

Abstract: The paper is devoted to the study of the homogeneous Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions:ut=diva(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 suitable Sobolev–Orlicz spaces.

Keywords: Parabolic equation; Double nonlinearity; Variable nonlinearity; Nonstandard growth conditions (search for similar items in EconPapers)
Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2011:i:10:p:2018-2032

DOI: 10.1016/j.matcom.2010.12.015

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