Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures)Khayyam Journal of Mathematics2423-47887120210101Existence of renormalized solutions for a class of nonlinear parabolic equations with generalized growth in Orlicz spaces14016412305810.22034/kjm.2020.184027.1422ENMohamed BourahmaLaboratory of mathematical analysis and applications (LAMA),
Department of mathematics, Faculty of Sciences Dhar el Mahraz,
Sidi Mohamed Ben Abdellah University,
PB 1796 Fez-Atlas, Fez MoroccoAbdelmoujib BenkiraneLaboratory of mathematical analysis and applications (LAMA),
Department of mathematics, Faculty of Sciences Dhar el Mahraz,
Sidi Mohamed Ben Abdellah University,
PB 1796 Fez-Atlas, Fez MoroccoJaouad BennounaLaboratory of mathematical analysis and applications (LAMA),
Department of mathematics, Faculty of Sciences Dhar el Mahraz,
Sidi Mohamed Ben Abdellah University,
PB 1796 Fez-Atlas, Fez MoroccoJournal Article20190514In this study, we prove an existence result of renormalized<br /> solutions for nonlinear parabolic equations of the type<br /> $$<br /> \displaystyle\frac{\partial b(x,u)}{\partial t}<br /> -\mbox{div}\>a(x,t,u,\nabla u)-\mbox{div}\><br /> \Phi(x,t,u)=<br /> f \quad\mbox{in }{Q_T=\Omega\times (0,T)},<br /> $$<br /> 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<br /> on its conjugate $\overline{M}$.https://www.kjm-math.org/article_123058_ec70c31a8cafddd00c989b31bea2f469.pdf