No abstract

In this paper, we prove the existence and uniqueness of entropy solutions for the following equations in Orlicz spaces: where f is an element of L 1 (Q T) , the term − div a(x, ∇u(x, t)) is a Leray-Lions operator on W 1,x 0 L M (Ω) , with M(.) does not satisfy the Δ 2 condition and is a continuous non decreasing real function defined on ℝ with (0) = 0. The investigation is made by approximation of the Rothe method which is based on a semi-discretization of the given problem with respect to the time variable.