Global and blowup solutions for general Lotka-Volterra systems

Shaohua  Chen; Runzhang  Xu; Hongtao  Yang

doi:10.3934/cpaa.2016012

Article Contents

2016, Volume 15, Issue 5: 1757-1768. Doi: 10.3934/cpaa.2016012

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Global and blowup solutions for general Lotka-Volterra systems

1.
School of Science and Technology, Cape Breton University, Sydney, NS, Canada, B1P 6L2
2.
College of Science, Harbin Engineering University, Harbin 150001

Received: August 31, 2015

Revised: February 29, 2016

Published: August 2016

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Abstract

This paper deals with global and blowup solutions of the degenerate parabolic system $u_t=\alpha(v)\nabla\cdot(u^{p}\nabla u)+f(u,v)$ and $v_t=\beta(u)\nabla\cdot(v^{q}\nabla v)+g(u,v)$ with homogeneous Dirichlet boundary conditions. We will give sufficient conditions such that the solutions either exist globally or blow up in a finite time. In special cases, a necessary and sufficient condition for the global existence is given.

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Mathematics Subject Classification: Primary: 35K10, 35K55; Secondary: 35C53.

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