Existence of solutions to a periodic parabolic problem with Orlicz growth and L^{۱} data

In  this paper, we are concerned with the  existence  of renormalized solution for a  nonlinear periodic  parabolic problem associated to the equation\begin{equation}\frac{\partial u}{\partial t}-A(u)+g(x,t,u,\nabla u)=f\in L^{۱} \end{equation}where  A(u) is the  m-Laplacian operator defined on  W^{۱,x}_{۰}L_{M}(\mathcal{Q}).

Keywords:

Periodic solutions , Orlicz space , Renormalized solutions , L^{۱} data , Weak solutions , ۳۵B۱۰ , ۳۵K۵۵