Blow-up for an evolution p-laplace system with nonlocal sources and inner absorptions

Abstract

Abstract This paper investigates the blow-up properties of positive solutions to the following system of evolution p-Laplace equations with nonlocal sources and inner absorptions { u t − div ( | ∇ u | p − 2 ∇ u ) = ∫ Ω v m d x − α u r , x ∈ Ω , t > 0, v t − div ( | ∇ v | q − 2 ∇ v ) = ∫ Ω u n d x − β v s , x ∈ Ω , t > 0 with homogeneous Dirichlet boundary conditions in a smooth bounded domain Ω ∈ R N (N ≥ 1), where p, q > 2, m, n, r, s ≥ 1, α, β > 0. Under appropriate hypotheses, the authors discuss the global existence and blow-up of positive weak solutions by using a comparison principle. 2010 Mathematics Subject Classification: 35B35; 35K60; 35K65; 35K57.