@article {
author = {Bourahma, Mohamed and Benkirane, Abdelmoujib and Bennouna, Jaouad},
title = {Existence of renormalized solutions for a class of nonlinear parabolic equations with generalized growth in Orlicz spaces},
journal = {Khayyam Journal of Mathematics},
volume = {7},
number = {1},
pages = {140-164},
year = {2021},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.184027.1422},
abstract = {In this study, we prove an existence result of renormalized solutions for nonlinear parabolic equations of the type $$ \displaystyle\frac{\partial b(x,u)}{\partial t} -\mbox{div}\>a(x,t,u,\nabla u)-\mbox{div}\> \Phi(x,t,u)= f \quad\mbox{in }{Q_T=\Omega\times (0,T)}, $$ where $b(x,\cdot)$ is a strictly increasing $C^1$-function for every $x\in\Omega$ with $b(x,0)=0$, the lower order term $\Phi$ satisfies a natural growth condition described by the appropriate Orlicz function $M$ and $f$ is an element of $L^1(Q_T)$. We don't assume any restriction neither on $M$ nor on its conjugate $\overline{M}$.},
keywords = {Parabolic problem,Orlicz spaces,Renormalized solutions,Generalized growth},
url = {http://www.kjm-math.org/article_123058.html},
eprint = {http://www.kjm-math.org/article_123058_ec70c31a8cafddd00c989b31bea2f469.pdf}
}