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Journal of Scientific Computing

Erschienen in:

01.06.2015

A Numerical Comparison Between Degenerate Parabolic and Quasilinear Hyperbolic Models of Cell Movements Under Chemotaxis

verfasst von: Roberto Natalini, Magali Ribot, Monika Twarogowska

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2015

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Abstract

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on a quasilinear hyperbolic system with damping, the other one on a degenerate parabolic equation. The two models have the same stationary solutions, which may contain some regions with vacuum. We first explain in details how to discretize the quasilinear hyperbolic system through an upwinding technique, which uses an adapted reconstruction, which is able to deal with the transitions to vacuum. Then we concentrate on the analysis of asymptotic preserving properties of the scheme towards a discretization of the parabolic equation, obtained in the large time and large damping limit, in order to present a numerical comparison between the asymptotic behavior of these two models. Finally we perform an accurate numerical comparison of the two models in the time asymptotic regime, which shows that the respective solutions have a quite different behavior for large times.

Vorheriger Artikel Error Analysis of Explicit Partitioned Runge–Kutta Schemes for Conservation Laws

Nächster Artikel Well-Balanced Central Schemes on Overlapping Cells with Constant Subtraction Techniques for the Saint-Venant Shallow Water System

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Titel: A Numerical Comparison Between Degenerate Parabolic and Quasilinear Hyperbolic Models of Cell Movements Under Chemotaxis
verfasst von: Roberto Natalini
Magali Ribot
Monika Twarogowska
Publikationsdatum: 01.06.2015
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2015
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9909-y

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