Study of a chemo-repulsion model with quadratic production. Part I: Analysis of the continuous problem and time-discrete numerical schemes
We consider a chemo-repulsion model with quadratic production in a bounded domain. Firstly, we obtain global in time weak solutions, and give a regularity criterion (which is satisfied for 1D and 2D domains) to deduce uniqueness and global regularity. After, we study two cell-conservative and uncond...
| Autores: | , , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:dnet:idus________::bbe7892a04c4b61ba43497bbc07556ec |
| Acesso em linha: | https://hdl.handle.net/11441/186552 https://doi.org/10.1016/j.camwa.2020.04.009 |
| Access Level: | acceso abierto |
| Palavra-chave: | Chemo-repulsion model Quadratic production First-order time schemes Energy-stability Convergence Error estimates |
| Resumo: | We consider a chemo-repulsion model with quadratic production in a bounded domain. Firstly, we obtain global in time weak solutions, and give a regularity criterion (which is satisfied for 1D and 2D domains) to deduce uniqueness and global regularity. After, we study two cell-conservative and unconditionally energy-stable first-order time schemes: a (nonlinear and positive) Backward Euler scheme and a linearized coupled version, proving solvability, convergence towards weak solutions and error estimates. In particular, the linear scheme does not preserve positivity and the uniqueness of the nonlinear scheme is proved assuming small time step with respect to a strong norm of the discrete solution. This hypothesis is reduced to small time step in nD domains (n ≤ 2) where global in time strong estimates are proved. Finally, we show the behavior of the schemes through some numerical simulations. |
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