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.