Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Cooperative systems with any number of species


Authors: Manuel Delgado and Antonio Suárez
Journal: Quart. Appl. Math. 61 (2003), 683-699
MSC: Primary 35R50; Secondary 35K57, 92D25
DOI: https://doi.org/10.1090/qam/2019618
MathSciNet review: MR2019618
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Abstract: In this paper we study the positive solutions of a cooperative system of any number of equations which consider the case of the slow diffusion and include the Lotka-Volterra model. We determine conditions of existence of global solution and blow-up in finite time in terms of the value of the spectral radius of a certain nonnegative matrix associated to the system. The results generalize the ones known for the particular case of two equations and we justify them by using the specific properties of nonnegative matrices which translate the cooperative character of the system.


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DOI: https://doi.org/10.1090/qam/2019618
Article copyright: © Copyright 2003 American Mathematical Society


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