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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| Formato: | article |
| Lenguaje: | EN ES |
| Publicado: |
Pontificia Universidad Javeriana
2019
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/67e2bfb122cb462ea430bb2c516f2b06 |
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| Sumario: | 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. |
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