A reducing mechanism on wave speed for chemotaxis systems with degenerate diffusion

Shanming Ji, Zhi An Wang, Tianyuan Xu, Jingxue Yin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

This paper is concerned with traveling wave solutions for a chemotaxis model with degenerate diffusion of porous medium type. We establish the existence of semi-finite traveling waves, including the sharp type and C1 type semi-finite waves. Our results indicate that chemotaxis slows down the wave speed of semi-finite traveling wave, that is, the traveling wave speed for chemotaxis with porous medium (degenerate) diffusion is smaller than that for the porous medium equation without chemotaxis. As we know, this is a new result not shown in the existing literature. The result appears to be a little surprising since chemotaxis is a convective force. We prove our results by the Schauder’s fixed point theorem and estimate the wave speed by a variational approach.

Original languageEnglish
Article number178
Pages (from-to)1-19
Number of pages19
JournalCalculus of Variations and Partial Differential Equations
Volume60
Issue number5
DOIs
Publication statusPublished - Oct 2021

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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