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...

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Detalles Bibliográficos
Autores: Casabán Bartual, María Consuelo, Company Rossi, Rafael, Egorova, Vera|||0000-0002-3024-3033, Jódar Sánchez, Lucas
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
Descripción
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.