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 146
Existence of weak solutions for a class of nonlocal parabolic p(u)-Laplacian problem
Said Ait Temghart, Chakir Allalou, Khalid Hilal
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 20, 2022
March 03, 2133
April 15, 2133

Abstract: In this paper, we consider the existence of weak solutions for some parabolic p-Laplacian problem in the case where the exponent p may depend on the unknown solution itself. We consider the situation when p is a nonlocal quantity. Namely, we study the following parabolic problem: u_t-div(|∇u|^(p(b(u))-2) ∇u)=f+g(u) |∇u|^(p(b(u))-1) in Ω_T=Ω×(0,T) where Ω is a bounded domain of R^(N≥2), T>0,f is a given data and g is a bounded continuous function belongs to L^1 (R). The motivation to study these nonlocal problems relies in the fact that, in reality the measurements of some ...