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 136
On strongly quasilinear degenerate elliptic systems with weak monotonicity and nonlinear physical data
Hasnae El Hammar, Allalou Chakir, Said Melliani
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 19, 2022
March 03, 2125
April 15, 2125

Abstract: This article is devoted to studying the quasilinear elliptic system -div a(x,u,Du)+b(x,u,Du)=v(x)+f(x,u)+div g(x,u) on a bounded open domain, with homogeneous Dirichlet boundary conditions. We show that there is a weak solution to this system under regularity, growth, and coercivity conditions for a, but only with very moderate monotonicity assumptions. We prove the existence result by using Galerkin's approximation and the theory of Young measures.