TY - JOUR T1 - Existence of Renormalized Solutions for Nonlinear Parabolic Equations AU - Akdim , Youssef AU - Benkirane , A. AU - EL Moumni , M. AU - Redwane , Hicham JO - Journal of Partial Differential Equations VL - 1 SP - 28 EP - 49 PY - 2014 DA - 2014/03 SN - 27 DO - http://doi.org/10.4208/jpde.v27.n1.2 UR - https://global-sci.org/intro/article_detail/jpde/5124.html KW - Nonlinear parabolic equations KW - renormalized solutions KW - Sobolev spaces AB - We give an existence result of a renormalized solution for a class of nonlinear parabolic equations $$\frac{\partial b(x,u)}{\partial t}-div(a(x,t,u,\nabla u))+g(x,t,u,\nabla u)+H(x,t,\nabla u)=f,\qquad in\; Q_T,$$ where the right side belongs to $L^{p'}(0,T;W^{-1,p'}(Ω))$ and where b(x,u) is unbounded function of u and where $-div(a(x,t,u,∇u))$ is a Leray-Lions type operatorwith growth $|∇u|^{p-1}$ in ∇u. The critical growth condition on g is with respect to ∇u and no growth condition with respect to u, while the function $H(x,t,∇u)$ grows as $|∇u|^{p-1}$.