Travelling Chemotactic Aggregates at Mesoscopic Scale and BiStability
| Autor: | Vincent Calvez, Monika Twarogowska, Laurent Gosse |
|---|---|
| Přispěvatelé: | Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Istituto per le Applicazioni del Calcolo 'Mauro Picone' (IAC), National Research Council of Italy | Consiglio Nazionale delle Ricerche (CNR), Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), European Project: 639638,H2020,ERC-2014-STG,MESOPROBIO(2015), Institut Camille Jordan [Villeurbanne] (ICJ), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Consiglio Nazionale delle Ricerche [Roma] (CNR), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2017 |
| Předmět: |
0301 basic medicine
Scale (ratio) Bistability exponential layers Motion (geometry) solitary wave Run-and-tumble model 65M06 92C45 Bifurcation diagram 03 medical and health sciences Stability theory [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] chemotaxis Well-balanced scheme AMS subject classifications 35Q92 Physics Mesoscopic physics Applied Mathematics kinetic model 92C37 Exponential function run-and-tumble Well-balanced scheme 030104 developmental biology Classical mechanics Kinetic equations |
| Zdroj: | SIAM Journal on Applied Mathematics SIAM journal on applied mathematics 77 (2017): 2224–2249. doi:10.1137/16M1108108 info:cnr-pdr/source/autori:Vincent Calvez; Laurent Gosse; Monika Twarogowska/titolo:TRAVELLING CHEMOTACTIC AGGREGATES AT MESOSCOPIC SCALE AND BISTABILITY/doi:10.1137%2F16M1108108/rivista:SIAM journal on applied mathematics (Print)/anno:2017/pagina_da:2224/pagina_a:2249/intervallo_pagine:2224–2249/volume:77 SIAM Journal on Applied Mathematics, 2017, 77 (6), pp.2224-2249 SIAM Journal on Applied Mathematics, Society for Industrial and Applied Mathematics, 2017, 77 (6), pp.2224-2249 |
| ISSN: | 0036-1399 |
| DOI: | 10.1137/16M1108108 |
| Popis: | International audience; We investigate numerically a model consisting in a kinetic equation for the biased motion of bacteria following a run-and-tumble process, coupled with two reaction-diffusion equations for chemical signals. This model exhibits asymptotic propagation at a constant speed. In particular, it admits travelling wave solutions. To capture this propagation, we propose a well-balanced numerical scheme based on Case's elementary solutions for the kinetic equation, and L-splines for the parabolic equations. We use this scheme to explore the Cauchy problem for various parameters. Some examples far from the diffusive regime lead to the coexistence of two waves travelling at different speeds. Numerical tests support the hypothesis that they are both locally asymptotically stable. Interestingly, the exploration of the bifurcation diagram raises counter-intuitive features. |
| Databáze: | OpenAIRE |
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