Parabolic equations with double variable nonlinearities

摘要

The paper is devoted to the study of the homogeneous Dirichlet problem for the doubly nonlinear parabolic equation with nonstandard growth conditions: u_t = div (a(x, t, u)|u|~(α(x,t))▽u|~(ρ(x,t)-2)▽u) + f(x, t) with given variable exponents α(x, t) and ρ(x, t). We establish conditions on the data which guarantee the existence of bounded weak solutions in suitable Sobolev-Orlicz spaces.