Parabolic equations with double variable nonlinearities

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.

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Year of publication:	2011
Authors:	Antontsev, S. ; Shmarev, S.
Published in:	Mathematics and Computers in Simulation (MATCOM). - Elsevier, ISSN 0378-4754. - Vol. 81.2011, 10, p. 2018-2032
Publisher:	Elsevier
Subject:	Parabolic equation \| Double nonlinearity \| Variable nonlinearity \| Nonstandard growth conditions

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011050502