Global existence and asymptotic stability of self-similar solutions for the fractional chemotaxis model

CAI Zhongbo; ZHAO Jihong; LUO Yongke

doi:10.13471/j.cnki.acta.snus.2022A005

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Global existence and asymptotic stability of self-similar solutions for the fractional chemotaxis model

Research articles | 更新时间：2023-11-01

- Global existence and asymptotic stability of self-similar solutions for the fractional chemotaxis model
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 62, Issue 2, Pages: 181-188(2023)
- 作者机构：
  
  宝鸡文理学院数学与信息科学学院，陕西宝鸡 721013
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2022A005
  CLC： O175.21
- Received：10 January 2022，
  
  Accepted：21 February 2022，
  
  Online First：30 December 2022，
  
  Published：25 March 2023
- 稿件说明：
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蔡中博,赵继红,罗永轲.分数阶趋化模型自相似解的整体存在性和渐近稳定性[J].中山大学学报(自然科学版),2023,62(02):181-188.

CAI Zhongbo,ZHAO Jihong,LUO Yongke.Global existence and asymptotic stability of self-similar solutions for the fractional chemotaxis model[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(02):181-188.
蔡中博,赵继红,罗永轲.分数阶趋化模型自相似解的整体存在性和渐近稳定性[J].中山大学学报(自然科学版),2023,62(02):181-188. DOI： 10.13471/j.cnki.acta.snus.2022A005.

CAI Zhongbo,ZHAO Jihong,LUO Yongke.Global existence and asymptotic stability of self-similar solutions for the fractional chemotaxis model[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2023,62(02):181-188. DOI： 10.13471/j.cnki.acta.snus.2022A005.

摘要

主要考虑了一类分数阶趋化模型，是生物学中描述趋化现象的Keller-Segel模型的推广模型。基于热半群在伪测度空间中的线性和非线性估计，建立了该模型自相似解的整体存在性和唯一性。还利用Lebesgue控制收敛定理建立了该模型自相似解当时间趋于无穷时的渐近稳定性。

Abstract

A class of fractional chemotaxis model is concerned， which is a generalized model of the Keller-Segel equations arising from biology in describing chemotaxis phenomenon. Based on the linear and nonlinear estimates of the heat semi-group in the pseudo-measure space， the global existence and uniqueness of self-similar solutions are established. Moreover， by applying the Lebesgue dominated convergence theorem， the asymptotic stability of self-similar solutions are also established as time tends to infinity.

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references

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