%0 Journal Article
%T Existence of renormalized solutions for a class of nonlinear parabolic equations with generalized growth in Orlicz spaces
%J Khayyam Journal of Mathematics
%I 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)
%Z 2423-4788
%A Bourahma, Mohamed
%A Benkirane, Abdelmoujib
%A Bennouna, Jaouad
%D 2021
%\ 01/01/2021
%V 7
%N 1
%P 140-164
%! Existence of renormalized solutions for a class of nonlinear parabolic equations with generalized growth in Orlicz spaces
%K Parabolic problem
%K Orlicz spaces
%K Renormalized solutions
%K Generalized growth
%R 10.22034/kjm.2020.184027.1422
%X 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 $\overline{M}$.
%U http://www.kjm-math.org/article_123058_ec70c31a8cafddd00c989b31bea2f469.pdf