TY - JOUR
T1 - A reducing mechanism on wave speed for chemotaxis systems with degenerate diffusion
AU - Ji, Shanming
AU - Wang, Zhi An
AU - Xu, Tianyuan
AU - Yin, Jingxue
N1 - Funding Information:
The research of S. Ji is supported by Guangdong Basic and Applied Basic Research Foundation Grant No. 2021A1515010367. The research of Z.A. Wang is supported by Hong Kong RGC GRF grant PolyU 153055/18P (Project ID P0005472). The research of T. Xu is supported by China Postdoctoral Science Foundation No. 2021M691070. The research of J. Yin was supported by NSFC Grant Nos. 11771156 & 12026220, Guangdong Basic and Applied Basic Research Foundation Grant No. 2020B1515310013, Science and Technology Program of Guangzhou No. 2019050001, and NSF of Guangzhou Grant No. 201804010391.
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2021/10
Y1 - 2021/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85111511800&partnerID=8YFLogxK
U2 - 10.1007/s00526-021-01990-y
DO - 10.1007/s00526-021-01990-y
M3 - Journal article
AN - SCOPUS:85111511800
SN - 0944-2669
VL - 60
SP - 1
EP - 19
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 5
M1 - 178
ER -