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: $$\frac{\partial u}{\partial t}-div(a(x,t, abla u))=f(x,t)$$ where $-div(a (x,t, abla u))$ is a Leray-Lions operator defined on a subset of $W^{1,x}_{0}L_{M}(Q)$. The $\Delta_{2}$-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. Mathematics Subject Classification (2010): 35B10, 35A01, 35D30. Received 26 August 2023; Accepted 05 February 2024.