Global Weak Solutions and Asymptotics of a 3D  Chemotaxis System

Tang Hao-yi; Peng Hong-yun

doi:10.12052/gdutxb.200148

English Version Journal Login

您当前的位置：

首页 >

文章列表页 >

Global Weak Solutions and Asymptotics of a 3D Chemotaxis System

更新时间：2026-05-27

- Global Weak Solutions and Asymptotics of a 3D Chemotaxis System
- Vol. 39, Issue 1, Pages: 93-98(2022)
- 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：
- 基金信息：
- DOI：10.12052/gdutxb.200148
  CLC： O175
- Published：2022
- 稿件说明：
移动端阅览
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.

关键词

Keywords

references

DENG C, LI T. Well-posedness of a 3D parabolic-hyperbolic Keller-Segel system in the Sobolev space framework [J]. Journal of Differential Equations, 2014, 257(5): 1311-1332.

WANG Z A, XIANG Z, YU P. Asymptotic dynamics on a singular chemotaxis system modeling onset of tumor angiogenesis [J]. Journal of Differential Equations, 2016, 260(3): 2225-2258.

GRANERO-BELINCHÓN R. Global solutions for a hyperbolic-parabolic system of chemotaxis [J]. Journal of Mathematical Analysis and Applications, 2017, 449(1): 872-883.

HOU Q Q, LIU C J, WANG Y G, et al . Stability of boundary layers for a viscous hyperbolic system arising from chemotaxis: one dimensional case [J ] . SIAM Journal on Mathematical Analysis, 2018, 50(3): 3058-3091.

CORRIAS L, PERTHAME B, ZAAG H. A chemotaxis model motivated by angiogenesis [J]. Comptes Rendus Mathématique Académie des Sciences Paris, 2003, 336(2): 141-146.

LEVINE H A, SLEEMAN B D. A system of reaction diffusion equations arising in the theory of reinforced random walks [J]. SIAM Journal on Applied Mathematics, 1997, 57(3): 683-730.

MEI M, PENG H, WANG Z A. Asymptotic profile of a parabolic-hyperbolic system with boundary effect arising from tumor angiogenesis [J]. Journal of Differential Equations, 2015, 259(10): 5168-51,91.

GUO J, XIAO J X, ZHAO H J, et al . Global solutions to a hyperbolic-parabolic coupled system with large initial data[J ] . Acta Mathematica Scientia, 2009, 29(3): 629-641.

LI D, PAN R, ZHAO K. Quantitative decay of a hybrid type chemotaxis model with large data [J]. Nonlinearity, 2015, 28: 2181-2210.

MARTINEZ V, WANG Z A, ZHAO K. Asymptotic and viscous stability of large-amplitude solutions of a hyperbolic system arising from biology [J]. Indiana University Mathematics Journal, 2018, 67(4): 1383-1424.

LI T, PAN R H, ZHAO K. Global dynamics of a chemotaxis model on bounded domains with large data [J]. SIAM Journal on Applied Mathematics, 2012, 72: 417-443.

CHAE M, CHOI K, KANG K, et al . Stability of planar traveling waves in a Keller-Segel equation on an infinite strip domain [J ] . Journal of Differential Equations, 2018, 265(1): 237-279.

LI D, LI T, ZHAO K. On a hyperbolic-parabolic system modeling chemotaxis [J]. Mathematical Models and Methods in Applied Sciences, 2011, 21(8): 1631-1650.

FAN J, ZHAO K. Blow up criteria for a hyperbolic-parabolic system arising from chemotaxis [J]. Journal of Mathematical Analysis and Applications, 2012, 394: 687-695.

PENG H Y, WANG Z A. On a parabolic-hyperbolic chemotaxis system with discontinuous data: well- posedness, stability and regularity[J]. Journal of Differential Equations, 2020, 268(8): 4374-4 415.

HOFF D. Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data [J]. Archive for Rational Mechanics and Analysis, 1995, 132(1): 1-14.

FRIEDMAN A. Partial Differential Equations[M]. New York: Holt, Rinehart Winston, 1969: 2-11.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Stability and Boundedness of a Class of Thirdorder Delay Differential Equations

Asymptotic Stability of Nonlinear Differential Equation with Time Delays

The Asymptotic Stability of Networks with Leakage Delays

A Study of Power Quality Regulation Strategies of Energy Storage Converters

An Optimal Operation Strategy for Community Microgrid Alliances Considering Power Exchange under Multi-package Shared Energy Storage Model

Related Author

Xu Lin

Song Chang-xiu

Huang Ming-hui

Xie Zu-wei

Peng Shi-guo

Luo Ying-hua

Related Institution

No data

AI问答

⁰