Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 250
Some nonlinear parabolic problems with singular natural growth term
Mounim El Ouardy, Youssef El Hadfi
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 28, 2022
March 03, 2221
April 15, 2221

Abstract: In this paper, we study the existence and regularity results for nonlinear parabolic problems with singular natural growth gradient terms $$ \left\lbrace \begin{array}{lll} \frac{\partial u}{\partial t}-\Delta_{p}u+b(x,t)\frac{|\nabla u|^{p}}{u^{\theta}}=f &\mbox{ in }& Q,\\ u(x,t)=0 & \mbox{ on }& \Gamma,\\ u(x,0)=0 &\mbox{ in }& \Omega, \end{array} \right. $$ where $\Omega$ is a bounded open subset of $\mathbb{R}^{N},$ $N\geq 2,$ $Q$ is the cylinder $\Omega\times (0,T),$ $T>0,$ $\Gamma$ the lateral surface $\partial\Omega\times (0,T),$ $\Delta_{p}$ is the so-called ...