Existence of solutions to a periodic parabolic problem with Orlicz growth and $L^{1}$ data

Document Type : Review articles


1 Sidi Mohamed Ben Abdellah University Faculty of Sciences Dhar el Mahraz, Laboratory of Mathematical Analysis and Applications, Fez, Morocco

2 CRMEF F\es, Morocco


In  this paper, we are concerned with the  existence  of renormalized solution for a  nonlinear periodic  parabolic problem associated to the equation
\frac{\partial u}{\partial t}-A(u)+g(x,t,u,\nabla u)=f\in L^{1} 
where  $A(u)$ is the  m-Laplacian operator defined on $ W^{1,x}_{0}L_{M}(\mathcal{Q})$.


Volume 14, Issue 1
January 2023
Pages 1557-1575
  • Receive Date: 01 October 2022
  • Revise Date: 21 December 2022
  • Accept Date: 29 December 2022