@Article{JPDE-27-1,
author = {Youssef, Akdim and Redwane, Hicham and Benkirane, A. and Moumni, M., EL and Redwane, Hicham},
title = {Existence of Renormalized Solutions for Nonlinear Parabolic Equations},
journal = {Journal of Partial Differential Equations},
year = {2014},
volume = {27},
number = {1},
pages = {28--49},
abstract = { 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 $|∇u|^{p-1}$.},
issn = {2079-732X},
doi = {https://doi.org/10.4208/jpde.v27.n1.2},
url = {https://global-sci.com/article/88291/existence-of-renormalized-solutions-for-nonlinear-parabolic-equations}
}