文献类型：期刊文献

英文题名：Global solution for a kinetic chemotaxis model with internal dynamics and its fast adaptation limit

作者：Liao, Jie[1]

机构：[1]E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

年份：2015

卷号：259

期号：11

起止页码：6432

外文期刊名：JOURNAL OF DIFFERENTIAL EQUATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000367755900029)】；

基金：This work is mentored by Professor Benoit Perthame during the author's visit to Laboratoire Jacques-Louis Lions, UPMC, France. Professor Benoit Perthame provided lots of fruitful suggestions and essential help. The author is deeply indebted to him for his hospitality and generous help. The author would also like to acknowledge the important comments and suggestions provided by Professor Nicola Bellomo which greatly improved a previous version of this work. The research is partially support by National Natural Science Foundation of China (No. 11301182), and Science and Technology Commission of Shanghai Municipality (No. 13ZR1453400).

语种：英文

外文关键词：Kinetic chemotaxis model; Internal dynamics; Global solution; Fast adaptation limit

摘要：A nonlinear kinetic chemotaxis model with internal dynamics incorporating signal transduction and adaptation is considered. This paper is concerned with: (i) the global solution for this model, and, (ii) its fast adaptation limit to Othmer Dunbar Alt type model. This limit gives some insight to the molecular origin of the chemotaxis behaviour. First, by using the Schauder fixed point theorem, the global existence of weak solution is proved based on detailed a priori estimates, under quite general assumptions. However, the Schauder theorem does not provide uniqueness, so additional analysis is required to be developed for uniqueness. Next, the fast adaptation limit of this model is derived by extracting a weak convergence subsequence in measure space. For this limit, the first difficulty is to show the concentration effect on the internal state. Another difficulty is the strong compactness argument on the chemical potential, which is essential for passing the nonlinear kinetic equation to the weak limit. (C) 2015 Elsevier Inc. All rights reserved.