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Open Access Research

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

Yan Zhang1, Dengming Liu2*, Chunlai Mu2 and Pan Zheng2

Author Affiliations

1 School of Mathematics and Computer Engineering, Xihua University, Chengdu, Sichuan 610039, PR China

2 College of Mathematics and Statistics, Chongqing University, Chongqing 410031, PR China

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Boundary Value Problems 2011, 2011:29  doi:10.1186/1687-2770-2011-29

Published: 6 October 2011

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

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2011/1/29/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2011/1/29/mathml/M1">View MathML</a>

with homogeneous Dirichlet boundary conditions in a smooth bounded domain Ω ∈ RN(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.

Keywords:
evolution p-Laplace system; global existence; blow-up; nonlocal sources; absorptions