Extinction behavior of solutions for a quasilinear parabolic system with nonlocal sources

Abstract

This paper deals with the extinction properties of solutions for a quasilinear parabolic systemut=div(|∇u|p-2∇u)+∫Ωvα(x,t)dx,vt=div(|∇v|q-2∇v)+∫Ωuβ(x,t)dxwith zero Dirichlet boundary conditions in a smooth bounded domain Ω⊂RN(N⩾1), where 1<p,q<2 and α,β>0. By using the comparison principle and energy estimate methods, we obtain the sufficient conditions of extinction solutions.