Existence and uniqueness of renormalized solution for nonlinear parabolic equations in Musielak Orlicz spaces

This paper is devoted to the study of a class of parabolic equation of type$$ \frac{\partial u}{\partial t} -div(A(x,t,u,\nabla u) +B(x,t,u)) =f \quad\mbox{in}\quad Q_T, $$where $div(A(x,t,u,\nabla u)$ is a Leray-Lions type operator, $B(x,t,u)$ is a nonlinear lower order term and $f\in L^{1}(Q_{T})$.We show the existence and the uniqueness of renormalized solution in the framework of Musielak-Orlicz spaces.