三维趋化系统全局弱解的存在性和渐近稳定性

唐浩怡; 彭红云

doi:10.12052/gdutxb.200148

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三维趋化系统全局弱解的存在性和渐近稳定性

综合研究 | 更新时间：2026-05-27

- 三维趋化系统全局弱解的存在性和渐近稳定性
- Global Weak Solutions and Asymptotics of a 3D Chemotaxis System
- 广东工业大学学报 2022年39卷第1期页码：93-98
- 作者机构：
  
  广东工业大学数学与统计学院,广东,广州,510520
- 作者简介：
  
  唐浩怡(1995–)，女，硕士研究生，主要研究方向为非线性偏微分方程
  彭红云(1984–)，男，副教授，主要研究方向为非线性偏微分方程， E-mail：hypengmath@gdut.edu.cn
- 基金信息：
  
  国家自然科学基金资助项目(11901115);广东省自然科学基金资助项目(2019A1515010706);广东工业大学青年百人启动项目(220413228)
- DOI：10.12052/gdutxb.200148
  中图分类号： O175
- 纸质出版：2022
- 稿件说明：
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唐浩怡, 彭红云. 三维趋化系统全局弱解的存在性和渐近稳定性[J]. 广东工业大学学报, 2022, 39(1): 93-98.

Tang Hao-yi, Peng Hong-yun. Global Weak Solutions and Asymptotics of a 3D Chemotaxis System[J]. 2022, 39(1): 93-98.
唐浩怡, 彭红云. 三维趋化系统全局弱解的存在性和渐近稳定性[J]. 广东工业大学学报, 2022, 39(1): 93-98. DOI： 10.12052/gdutxb.200148.

Tang Hao-yi, Peng Hong-yun. Global Weak Solutions and Asymptotics of a 3D Chemotaxis System[J]. 2022, 39(1): 93-98. DOI： 10.12052/gdutxb.200148.

摘要

主要研究了一类抛物−双曲型系统在不连续初值下全局弱解的适定性和大时间行为。该系统是利用Cole-Hopf变换从描述肿瘤血管生成的三维PDE-ODE (Partial Differential Equations-Ordinary Differential Equations )趋化模型转换而来的。本文在不连续初值条件下

证明了当时间趋于无穷时抛物−双曲型系统的解收敛于常数稳态解。

Abstract

The well-posedness and large-time behavior for a parabolic-hyperbolic system with discontinuous initial value is mainly considered. The system is transformed from a three dimensional PDE-ODE hybrid chemotaxis system describing the initiation of tumor angiogenesis by a Cole-Hopf type transformation. With discontinuous data

it is proved that the solution of the transformed system converges to a constant equilibrium as time tends to infinity. Lastly

the results for the pre-transformed PDE-ODE hybrid system are obtained by reversing the Cole-Hopf transformation. Compared with the relevant results on continuous initial datum

the asymptotic stability of discontinuous initial values with large oscillations is proved. In the proof

the so-called “effective viscous flux” is used for the analysis to obtain the desired energy estimates and regularity. The "effective viscous flux" technique is rarely used in the literature of chemotaxis model. But it has proved to be a useful tool for studying chemotaxis systems with initial datum having low regularity.

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Keywords

references

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