Theoretical and numerical analysis for a hybrid tumor model with diffusion depending on vasculature
In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes an anisotropic nonlinear diffusion term with a diffusion velocity increasing with respect to vasculature. First, we prove the existence of global in time weak-strong solutions using a regularization t...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2021 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::3c6334ff00c5e9f4aaf3be044bb9a630 |
| Acceso en línea: | https://hdl.handle.net/11441/186511 https://doi.org/10.1016/j.jmaa.2021.125325 |
| Access Level: | acceso abierto |
| Palabra clave: | Tumor model Glioblastoma PDE-ODE system Numerical scheme |
| Sumario: | In this work we analyse a PDE-ODE problem modelling the evolution of a Glioblastoma, which includes an anisotropic nonlinear diffusion term with a diffusion velocity increasing with respect to vasculature. First, we prove the existence of global in time weak-strong solutions using a regularization technique via an artificial diffusion in the ODE-system and a fixed point argument. In addition, stability results of the critical points are given under some constraints on parameters. Finally, we design a fully discrete finite element scheme for the model which preserves the pointwise and energy estimates of the continuous problem. |
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