TY - JOUR
ID - 123058
TI - Existence of renormalized solutions for a class of nonlinear parabolic equations with generalized growth in Orlicz spaces
JO - Khayyam Journal of Mathematics
JA - KJM
LA - en
SN -
AU - Bourahma, Mohamed
AU - Benkirane, Abdelmoujib
AU - Bennouna, Jaouad
AD - Laboratory 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 Morocco
Y1 - 2021
PY - 2021
VL - 7
IS - 1
SP - 140
EP - 164
KW - Parabolic problem
KW - Orlicz spaces
KW - Renormalized solutions
KW - Generalized growth
DO - 10.22034/kjm.2020.184027.1422
N2 - 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 $\overline{M}$.
UR - http://www.kjm-math.org/article_123058.html
L1 - http://www.kjm-math.org/article_123058_ec70c31a8cafddd00c989b31bea2f469.pdf
ER -