Renormalized Solution for a nonlinear parabolic problems with noncoercivity in divergence form in Orlicz Spaces

•We prove the existence result in the setting of Orlicz-Sobolev Spaces.•The N-function M does not satisfy the Δ2-condition.•Existence of a renormalized solution for a class of nonlinear parabolic equations.•The data belongs to L1 and no continuous assumption is made on divergence form.

In this paper we prove the existence results for renormalized solution of the following nonlinear parabolic problems in Orlicz-Sobolev Spaces (1)(P)∂b(x,u)∂t-diva(x,t,u,∇u)-div(Φ(x,t,u))=finQT=Ω×(0,T)b(u)(t=0)=b(u0)inΩu=0on∂Ω×(0,T),where b(x,u) is unbounded function of u, the term -diva(x,t,u,∇u) is a Leray-Lions operator defined on a subset of W01,xLM(QT), where M is a N-function without assuming a Δ2-condition, the second term f∈L1(QT) and Φ is a noncoercive function which satisfies only the growth condition.