Strongly nonlinear periodic parabolic equation in Orlicz spaces
Erriahi Elidrissi Ghita, Elhoussine Azroul, Abdelilah Lamrani Alaoui · Studia Universitatis Babes-Bolyai Matematica · 2025
In this paper, we prove the existence of a weak solution to the following nonlinear periodic parabolic equations in Orlicz-spaces: ∂u/∂t− div(a(x,t,∇u)) = f(x, t)where −div(a(x, t,∇u)) is a Leray-Lions operator defined on a subset of \(W^{1,x}_{0} L_{M}(Q)\). The Δ2-condition is not assumed and the data f belongs to \(W{−1,x}E_{\overline{M}}(Q)\). The Galerkin method and the fixed point argument are employed in the proof.