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 $|∇u|^{p-1}$.