Qualitative numerical analysis of a free-boundary diffusive logistic model
A two-dimensional free-boundary diffusive logistic model with radial symmetry is considered. This model is used in various fields to describe the dynamics of spreading in different media: fire propagation, spreading of population or biological invasions. Due to the radial symmetry, the free boundary...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad de Cantabria (UC) |
| Repositorio: | UCrea Repositorio Abierto de la Universidad de Cantabria |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unican.es:10902/30715 |
| Acceso en línea: | https://hdl.handle.net/10902/30715 |
| Access Level: | acceso abierto |
| Palabra clave: | Free-boundary problem Diffusive logistic model Radial symmetry Spreading–vanishing dichotomy Numerical analysis Finite-difference method |
| Sumario: | A two-dimensional free-boundary diffusive logistic model with radial symmetry is considered. This model is used in various fields to describe the dynamics of spreading in different media: fire propagation, spreading of population or biological invasions. Due to the radial symmetry, the free boundary can be treated by a front-fixing approach resulting in a fixed-domain non-linear problem, which is solved by an explicit finite difference method. Qualitative numerical analysis establishes the stability, positivity and monotonicity conditions. Special attention is paid to the spreading-vanishing dichotomy and a numerical algorithm for the spreading-vanishing boundary is proposed. Theoretical statements are illustrated by numerical tests. |
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