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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| Format: | Article |
| Language: | English |
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Pontificia Universidad Javeriana
2019-12-01
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| Series: | Universitas Scientiarum |
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| Online Access: | https://revistas.javeriana.edu.co/index.php/scientarium/article/view/23988 |
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| 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 |
| collection | DOAJ |
| 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 |
| id | doaj-art-67e2bfb122cb462ea430bb2c516f2b06 |
| institution | OA Journals |
| issn | 0122-7483 2027-1352 |
| language | English |
| publishDate | 2019-12-01 |
| publisher | Pontificia Universidad Javeriana |
| record_format | Article |
| series | Universitas Scientiarum |
| spelling | doaj-art-67e2bfb122cb462ea430bb2c516f2b062025-08-20T02:15:41ZengPontificia Universidad JaverianaUniversitas Scientiarum0122-74832027-13522019-12-0124356558710.11144/Javeriana.SC24-3.eolaExistence of local and global solution for a spatio-temporal predator-prey modelRicardo Cano Macias, Jorge Mauricio Ruiz V0Engineering Faculty, Universidad de La Sabana, Chía, Cundinamarca, Colombia, Mathematics Department, Universidad Nacional de Colombia, Bogotá D.C., Colombia.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.https://revistas.javeriana.edu.co/index.php/scientarium/article/view/23988global weak solution; iterative method; predator-prey system. |
| spellingShingle | Ricardo Cano Macias, Jorge Mauricio Ruiz V Existence of local and global solution for a spatio-temporal predator-prey model Universitas Scientiarum global weak solution; iterative method; predator-prey system. |
| title | 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_short | 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 |
| topic | global weak solution; iterative method; predator-prey system. |
| url | https://revistas.javeriana.edu.co/index.php/scientarium/article/view/23988 |
| work_keys_str_mv | AT ricardocanomaciasjorgemauricioruizv existenceoflocalandglobalsolutionforaspatiotemporalpredatorpreymodel |