Published Dec 6, 2019



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Ricardo Cano-Macias https://orcid.org/0000-0002-1701-7453

Jorge Mauricio Ruiz-Vera https://orcid.org/0000-0003-0677-4704

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Abstract

In this paper we prove the existence and uniqueness of weak solutions for a kind of Lotka–Volterra system, by using successive linearization techniques. This approach has the advantage to treat two equations separately in each iteration step. Under suitable initial conditions, we construct an invariant region to show the global existence in time of solutions for the system. By means of Sobolev embeddings and regularity results, we find estimates for predator and prey populations in adequate norms. In order to demonstrate the convergence properties of the introduced method, several numerical examples are given.

Keywords

global weak solution, iterative method, predator-prey system

References
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How to Cite
Cano-Macias, R., & Ruiz-Vera, J. M. (2019). Existence of local and global solution for a spatio-temporal predator-prey model. Universitas Scientiarum, 24(3), 565-587. https://doi.org/10.11144/Javeriana.SC24-3.eola
Section
Matemáticas y Estadística / Mathematics and Statistics / Matemática e Estatística