Year: 2014
Author: Youssef Akdim, Hicham Redwane, A. Benkirane, M. EL Moumni, Hicham Redwane
Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 1 : pp. 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 $|∇u|^{p-1}$.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v27.n1.2
Journal of Partial Differential Equations, Vol. 27 (2014), Iss. 1 : pp. 28–49
Published online: 2014-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Nonlinear parabolic equations