Existence of local and global solution for a spatio-temporal predator-prey model

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 inv...

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Autor principal:	Ricardo Cano Macias, Jorge Mauricio Ruiz V
Formato:	article
Lenguaje:	EN ES
Publicado:	Pontificia Universidad Javeriana 2019
Materias:	global weak solution; iterative method; predator-prey system. Science (General) Q1-390
Acceso en línea:	https://doaj.org/article/67e2bfb122cb462ea430bb2c516f2b06
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spelling	oai:doaj.org-article:67e2bfb122cb462ea430bb2c516f2b062021-11-16T16:41:23ZExistence of local and global solution for a spatio-temporal predator-prey model10.11144/Javeriana.SC24-3.eola0122-74832027-1352https://doaj.org/article/67e2bfb122cb462ea430bb2c516f2b062019-12-01T00:00:00Zhttps://revistas.javeriana.edu.co/index.php/scientarium/article/view/23988https://doaj.org/toc/0122-7483https://doaj.org/toc/2027-1352In 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.Ricardo Cano Macias, Jorge Mauricio Ruiz VPontificia Universidad Javerianaarticleglobal weak solution; iterative method; predator-prey system.Science (General)Q1-390ENESUniversitas Scientiarum, Vol 24, Iss 3, Pp 565-587 (2019)
institution	DOAJ
collection	DOAJ
language	EN ES
topic	global weak solution; iterative method; predator-prey system. Science (General) Q1-390
spellingShingle	global weak solution; iterative method; predator-prey system. Science (General) Q1-390 Ricardo Cano Macias, Jorge Mauricio Ruiz V Existence of local and global solution for a spatio-temporal predator-prey model
description	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.
format	article
author	Ricardo Cano Macias, Jorge Mauricio Ruiz V
author_facet	Ricardo Cano Macias, Jorge Mauricio Ruiz V
author_sort	Ricardo Cano Macias, Jorge Mauricio Ruiz V
title	Existence of local and global solution for a spatio-temporal predator-prey model
title_short	Existence of local and global solution for a spatio-temporal predator-prey model
title_full	Existence of local and global solution for a spatio-temporal predator-prey model
title_fullStr	Existence of local and global solution for a spatio-temporal predator-prey model
title_full_unstemmed	Existence of local and global solution for a spatio-temporal predator-prey model
title_sort	existence of local and global solution for a spatio-temporal predator-prey model
publisher	Pontificia Universidad Javeriana
publishDate	2019
url	https://doaj.org/article/67e2bfb122cb462ea430bb2c516f2b06
work_keys_str_mv	AT ricardocanomaciasjorgemauricioruizv existenceoflocalandglobalsolutionforaspatiotemporalpredatorpreymodel
_version_	1718426305488224256

Existence of local and global solution for a spatio-temporal predator-prey model

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