On the some equations inequalities in Musielak-Orlicz spaces with measure data

Abstract

Our aim in this present work is to prove the existence of a solution for the nonlinear unilateral parabolic problems associated to the equation ∂u - div a(x, t, u, ∇u) - div Φ(x, t, u) = μ in QT = Ω × (0, T), ∂t where the lower order term Φ satisfies a generalized natural growth condition and the datum μ belongs to L1(Q) + E (Q).