Strongly nonlinear periodic parabolic equation in Orlicz spaces - GHITA, Erriahi Elidrissi; ELHOUSSINE, Azroul; ABDELILAH, Lamrani Alaoui (Studia Universitatis Babeș-Bolyai Mathematica, 2025)
In this paper, we prove the existence of a weak solution to the following nonlinear periodic parabolic equations in Orlicz-spaces: ut-div(a(x,t, abla u))=f(x,t) where -div(a (x,t, abla u)) is a Leray-Lions operator defined on a subset of W^1,x_0L_M(Q). The Δ_2-condition is not assumed and the data f belongs to W^-1,xE_M (Q). The Galerkin method and the fixed point argument are employed in the proof. Mathematics Subject Classification (2010): 35B10, 35A01, 35D30. Received 26 August 2023; Accepted 05 February 2024.