Global boundedness and asymptotic behavior of solutions for a quasilinear chemotaxis model of multiple sclerosis with nonlinear signal secretion

Lu Xu; Chunlai Mu; Qiao Xin

doi:10.3934/dcdsb.2022118

Article Contents

2023, Volume 28, Issue 2: 1215-1243. Doi: 10.3934/dcdsb.2022118

This issue Previous Article Stability and dynamics of spike-type solutions to delayed Gierer-Meinhardt equations Next Article On the Campanato and Hölder regularity of local and nonlocal stochastic diffusion equations

Global boundedness and asymptotic behavior of solutions for a quasilinear chemotaxis model of multiple sclerosis with nonlinear signal secretion

1.
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
2.
College of Mathematics and Statistics, Yili Normal University, Yining 835000, China

^* Corresponding author: Lu Xu
^* Corresponding author: Lu Xu

Received: September 2021

Revised: April 2022

Early access: June 2022

Published: February 2023

The first author is supported by Natural Science Foundation of Xinjiang Autonomous Region under grant 2022D01C335 and Scientific Research Program of the Higher Education Institution of XinJiang [No.XJEDU2021Y043]. The second author is supported by NSFC under grants 11771062 and 11971082, the Fundamental Research Funds for the Central Universities under grant 2019CDJCYJ001 and 2020CDJQY-Z001, Chongqing Key Laboratory of Analytic Mathematics and Applications, Science and Technology Research Program of Chongqing Municipal Educational Commission(No.KJZD-M201900501)

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Abstract

The paper deals with the quasilinear parabolic-parabolic-ODE and parabolic-elliptic-ODE chemotaxis system with nonlinear signal secretion for multiple sclerosis and Boló's concentric sclerosis, respectively. Under appropriate assumptions on parameter, we study the global boundedness and asymptotic behavior of classical solutions to the problem. Our results improve or extend some results in [13] and [12].

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Mathematics Subject Classification: Primary: 35A01, 35K55, 35B40; Secondary: 92C17, 35Q92.

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References

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