@article{c88e29d92604432782bffe350f8c8661,
title = "Acceleration of Propagation in a Chemotaxis-growth System with Slowly Decaying Initial Data",
abstract = "In this paper, we study the spatial propagation dynamics of a parabolic–elliptic chemotaxis system with logistic source which reduces to the well-known Fisher-KPP equation without chemotaxis. It is known that for fast decaying initial functions, this system has a finite spreading speed. For slowly decaying initial functions, we show that the accelerating propagation will occur and chemotaxis does not affect the propagation mode determined by slowly decaying initial functions if the logistic damping is strong, that is, the system has the same upper and lower bounds of the accelerating propagation as for the classical Fisher-KPP equation. The main new idea of proving our results is the construction of auxiliary equations to overcome the lack of comparison principle due to chemotaxis.",
author = "Wang, {Zhi An} and Xu, {Wen Bing}",
note = "Funding Information: We thank the reviewers for their helpful comments. The research of Z.‐A. Wang is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administration Region of China (No. PolyU 153055/18P for GRF project) and an internal grant No. UAH0 (Project ID P0031504) from the Hong Kong Polytechnic University. The research of W.‐B. Xu was partially supported by China Postdoctoral Science Foundation funded project (2020T130679) and by the CAS AMSS‐POLYU Joint Laboratory of Applied Mathematics postdoctoral fellowship scheme. Funding Information: We thank the reviewers for their helpful comments. The research of Z.-A. Wang is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administration Region of China (No. PolyU 153055/18P for GRF project) and an internal grant No. UAH0 (Project ID P0031504) from the Hong Kong Polytechnic University. The research of W.-B. Xu was partially supported by China Postdoctoral Science Foundation funded project (2020T130679) and by the CAS AMSS-POLYU Joint Laboratory of Applied Mathematics postdoctoral fellowship scheme. Publisher Copyright: {\textcopyright} 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.",
year = "2023",
month = feb,
doi = "10.1112/blms.12738",
language = "English",
volume = "55",
pages = "447--469",
journal = "Bulletin of the London Mathematical Society",
issn = "0024-6093",
publisher = "John Wiley and Sons Ltd",
number = "1",
}