Communications in Mathematical Sciences

Volume 21 (2023)

Number 4

Global existence for quasilinear degenerate two-species chemotaxis system with small initial data

Pages: 967 – 996



Ke Lin (School of Economics and Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan, China)


This article is devoted to the analysis of quasilinear degenerate chemotaxis system with two-species in dimension $d \geq 3$. The global existence of weak solution to the chemotaxis system with small initial data is proved for the super-critical case in both parabolic-elliptic and fully parabolic types.


degenerate parabolic system, chemotaxis, global existence

2010 Mathematics Subject Classification

35A01, 35K65, 92C17

Received 11 June 2021

Received revised 2 August 2022

Accepted 30 August 2022

Published 24 March 2023