# American Institute of Mathematical Sciences

September  2016, 15(5): 1757-1768. doi: 10.3934/cpaa.2016012

## Global and blowup solutions for general Lotka-Volterra systems

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

Received  September 2015 Revised  March 2016 Published  July 2016

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.
Citation: Shaohua Chen, Runzhang Xu, Hongtao Yang. Global and blowup solutions for general Lotka-Volterra systems. Communications on Pure & Applied Analysis, 2016, 15 (5) : 1757-1768. doi: 10.3934/cpaa.2016012
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