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A hyperbolic model of chemotaxis on a network: a numerical study
- Source :
- ESAIM: Mathematical Modelling and Numerical Analysis, ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2014, 48 (1), pp.231-258, ESAIM: Mathematical Modelling and Numerical Analysis, 2014, 48 (1), pp.231-258, Modélisation mathématique et analyse numérique (En ligne) 48 (2014): 231–258. doi:10.1051/m2an/2013098, info:cnr-pdr/source/autori:G. Bretti, R. Natalini, and M. Ribot/titolo:A hyperbolic model of chemotaxis on a network: a numerical study/doi:10.1051%2Fm2an%2F2013098/rivista:Modélisation mathématique et analyse numérique (En ligne)/anno:2014/pagina_da:231/pagina_a:258/intervallo_pagine:231–258/volume:48
- Publication Year :
- 2014
- Publisher :
- EDP Sciences, 2014.
-
Abstract
- 25 pages; International audience; In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the behavior of solutions and to discuss the stability and the accuracy of our approximation.
- Subjects :
- Quantitative Biology::Tissues and Organs
Space dimension
transmission conditions
Stability (probability)
finite difference schemes
Quantitative Biology::Cell Behavior
Mathematics - Analysis of PDEs
hyperbolic system on network
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Applied mathematics
asymptotic behavior
Mathematics - Numerical Analysis
Numerical tests
chemotaxis
initial-boundary value problem
Mathematics
Numerical Analysis
Applied Mathematics
65M06, 35L50, 92B05, 92C17, 92C42
Chemotaxis
Numerical Analysis (math.NA)
Term (time)
Computational Mathematics
Transmission (telecommunications)
Modeling and Simulation
Scheme (mathematics)
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Analysis
Analysis of PDEs (math.AP)
Subjects
Details
- ISSN :
- 12903841 and 0764583X
- Volume :
- 48
- Database :
- OpenAIRE
- Journal :
- ESAIM: Mathematical Modelling and Numerical Analysis
- Accession number :
- edsair.doi.dedup.....cb8279a407496753270d54d79024ffec
- Full Text :
- https://doi.org/10.1051/m2an/2013098