一类经典趋化性模型行波解的存在性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (6): 1044-1058.

一类经典趋化性模型行波解的存在性

娄翠娟, 杨茵

华中科技大学数学与统计学院武汉 430074

收稿日期:2014-06-23 修回日期:2015-03-10 出版日期:2015-12-25 发布日期:2015-12-25
通讯作者: 杨茵,yangyin@mail.hust.edu.cn E-mail:yangyin@mail.hust.edu.cn
作者简介:娄翠娟,loucuijuan2006@126.com
基金资助:
国家自然科学基金(11071172,11471129)资助

Existence of Traveling Wave Solutions for a Classical Chemotaxis Model

Lou Cuijuan, Yang Yin

Department of Applied Mathematics, School of Mathematics and statistics, Huazhong University of Science and Technology, Wuhan 430074

Received:2014-06-23 Revised:2015-03-10 Online:2015-12-25 Published:2015-12-25

摘要/Abstract

摘要：

该文研究了一类经典趋化性模型Keller-Segel模型行波解的存在性.对Keller-Segel模型中的抛物-抛物型偏微分方程组和抛物型方程,该文研究了它们正行波解的存在性和波速.

关键词: 趋化性, Keller-Segel模型, 抛物-抛物型偏微分方程组, 抛物型方程, 行波解

Abstract:

In this paper, we study the existence of the traveling wave solutions for some Keller-Segel systems. For both parabolic-parabolic, and parabolic-differential types, we show the existence of the positive traveling wave solutions and investigate their speeds.

Key words: Chemotaxis, Keller-Segel model, Parabolic-parabolic, Parabolic-differential, Traveling wave solution

中图分类号:

O175.2

娄翠娟, 杨茵. 一类经典趋化性模型行波解的存在性[J]. 数学物理学报, 2015, 35(6): 1044-1058.

Lou Cuijuan, Yang Yin. Existence of Traveling Wave Solutions for a Classical Chemotaxis Model[J]. Acta mathematica scientia,Series A, 2015, 35(6): 1044-1058.

参考文献

[1] Keller E F, Segel L A. Initiation of slime mold aggregation viewed as an instability. Journal of Theoretical Biology, 1970, 26(3):399-415
[2] Othmer H G, Stevens A. Aggregation, blowup, and collapse:the ABCs of taxis in reinforced random walks. SIAM Journal on Applied Mathematics, 1997, 57(4):1044-1081
[3] Keller E F, Segel L A. Traveling bands of chemotactic bacteria:a theoretical analysis. Journal of Theoretical Biology, 1971, 30(2):235-248
[4] Rosen G. On the propagation theory for bands of chemotactic bacteria. Mathematical Biosciences, 1974, 20(1/2):185-189
[5] Keller E F, Odell G M. Necessary and sufficient conditions for chemotactic bands. Mathematical Biosciences, 1975, 27(3/4):309-317
[6] Nagai T, Ikeda T. Traveling waves in a chemotactic model. Journal of Mathematical Biology, 1991, 30(2):169-184
[7] Horstmann D, Stevens A. A constructive approach to traveling waves in chemotaxis. J Nonlinear Sci, 2004, 14(1):1-25
[8] Schwetlick H. Traveling waves for chemotaxis-systems. Proceedings in Applied Mathematics and Mechanics, 2003, 3(1):476-478
[9] 黎勇. 一类趋化性生物模型行波解的存在性. 应用数学学报, 2004, 27(1):123-131
[10] Xue C, Hwang H J, Painter K J, Erban R. Travelling waves in hyperbolic chemotaxis equations. Bull Math Biol, 2011,73(8):1695-1733
[11] 陈学勇,杨茵. 一类趋化性模型行波解的存在性. 数学学报, 2012, 55(5):817-828
[12] Li T, Wang Z A. Nonlinear stability of traveling waves to a hyperbolicparabolic system modeling chemotaxis. SIAM J Appl Math, 2009, 70(5):1522-1541
[13] Li T, Wang Z A. Asymptotic nonlinear stability of traveling waves to conservation laws arising from chemotaxis. J Differential Equations, 2011, 250:1310-1333
[14] Meyries M. Local well posedness and instability of travelling waves in a chemotaxis model. Adv Differential Equations, 2011, 16(1/2):31-60
[15] Wang Z A. Mathematics of traveling waves in chemotaxis. Discrete Contin Dyn Syst-Series B, 2013, 18(3):601-641
[16] 叶其孝等. 反应扩散方程引论. 北京:科学出版社, 1990