文献类型：期刊文献

英文题名：SYNCHRONISING AND NON-SYNCHRONISING DYNAMICS FOR A TWO-SPECIES AGGREGATION MODEL

作者：Emako-Kazianou, Casimir[1,2,3];Liao, Jie[4];Vauchelet, Nicolas[5]

机构：[1]UPMC Univ Paris 06, Sorbonne Univ, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France;[2]CNRS, UMR 7598, Lab Jacques Louis Lions, F-75005 Paris, France;[3]INRIA Paris Rocquencourt, EPC MAMBA, BP105, F-78153 Le Chesnay, France;[4]East China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China;[5]Univ Paris 13, Inst Galilee, LAGA, UMR 7539, 99 Ave Jean Baptiste Clement, F-93430 Villetaneuse, France

年份：2017

卷号：22

期号：6

起止页码：2121

外文期刊名：DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000402303900003)】；

基金：C. E.-K. and N. V. acknowledge partial support from the ANR project Kibord, ANR-13-BS01-0004 funded by the French Ministry of Research. J. L. would like to acknowledge partial support by Fundamental Research Funds for the Central Universities and a scholarship from China Scholarship Council for visiting Laboratoire Jacques-Louis Lions, UPMC, France.

语种：英文

外文关键词：Hydrodynamic limit; duality solution; two-species chemotaxis; aggregate dynamics; finite volume scheme

摘要：This paper deals with analysis and numerical simulations of a one-dimensional two-species hyperbolic aggregation model. This model is formed by a system of transport equations with nonlocal velocities, which describes the aggregate dynamics of a two-species population in interaction appearing for instance in bacterial chemotaxis. Blow-up of classical solutions occurs in finite time. This raises the question to define measure-valued solutions for this system. To this aim, we use the duality method developed for transport equations with discontinuous velocity to prove the existence and uniqueness of measure-valued solutions. The proof relies on a stability result. In addition, this approach allows to study the hyperbolic limit of a kinetic chemotaxis model. Moreover, we propose a finite volume numerical scheme whose convergence towards measure-valued solutions is proved. It allows for numerical simulations capturing the behaviour after blow up. Finally, numerical simulations illustrate the complex dynamics of aggregates until the formation of a single aggregate: after blow-up of classical solutions, aggregates of different species are synchronising or nonsynchronising when collide, that is move together or separately, depending on the parameters of the model and masses of species involved.