Well posedness and numerical solution of kinetic models for angiogenesis
Angiogenesis processes including the effect of stochastic branching and spread of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker-Planck type with a diffusion equation for the angiogenic factor. Well posedness studies underline the importan...
| Autores: | , , |
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| Tipo de recurso: | capítulo de libro |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/8839 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/8839 |
| Access Level: | acceso abierto |
| Palabra clave: | 519.8 Kinetic equations Difussion equations Positivity preserving schemes Stochastic models Investigación operativa (Matemáticas) Procesos estocásticos 1207 Investigación Operativa 1208.08 Procesos Estocásticos |
| Sumario: | Angiogenesis processes including the effect of stochastic branching and spread of blood vessels can be described coupling a (nonlocal in time) integrodifferential kinetic equation of Fokker-Planck type with a diffusion equation for the angiogenic factor. Well posedness studies underline the importance of preserving positivity when constructing approximate solutions. We devise order one positivity preserving schemes for a reduced model and show that soliton-like asymptotic solutions are correctly captured. We also find good agreement with the original stochastic model from which the deterministic kinetic equations are derived working with ensemble averages. Higher order positivity preserving schemes can be devised combining WENO and SSP procedures. |
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