✦ LIBER ✦

Shock formation in a chemotaxis model

✍ Scribed by Zhian Wang; Thomas Hillen

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 401 KB
Volume: 31
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.898

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✦ Synopsis

Abstract

In this paper, we establish the existence of shock solutions for a simplified version of the Othmer–Stevens chemotaxis model (SIAM J. Appl. Math. 1997; 57:1044–1081). The existence of these shock solutions was suggested by Levine and Sleeman (SIAM J. Appl. Math. 1997; 57:683–730). Here, we consider the general Riemann problem and derive the shock curves in parameterized forms. By studying the travelling wave solutions, we examine the shock structure for the chemotaxis model and prove that the travelling wave speed is identical to the shock speed. Moreover, we explicitly derive an entropy–entropy flux pair to prove the uniqueness of the weak shock solutions. Some discussion is given for further study. Copyright © 2007 John Wiley & Sons, Ltd.

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