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: u(1) = di upsilon (a(x, t, u)vertical bar u vertical bar(alpha(x,t)) vertical bar del u vertical bar(p(x,t)-2)del u) + f(x, t) with given variable exponents a(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. (C) 2011 IMACS. Published by Elsevier B.V. All rights reserved.
parabolic equation variable nonlinearity nonstandard growth conditions double nonlinearity