Convergence to nonlinear diffusion waves for a hyperbolic-parabolic chemotaxis system modelling vasculogenesis

被引：47

作者：

Liu, Qingqing ^{[1
]}

Peng, Hongyun ^{[2
]}

Wang, Zhi-An ^{[3
]}

机构：

[1] South China Univ Technol, Sch Math, Guangzhou 510641, Peoples R China

[2] Guangdong Univ Technol, Sch Math & Stat, Guangzhou 510006, Peoples R China

[3] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 314卷

基金：

中国国家自然科学基金;

关键词：

Chemotaxis; Hyperbolic-parabolic system; Diffusion wave; Asymptotic stability; COMPRESSIBLE EULER EQUATIONS; UNIPOLAR HYDRODYNAMIC MODEL; LARGE TIME BEHAVIOR; P-SYSTEM; ASYMPTOTIC-BEHAVIOR; CONSERVATION-LAWS; GLOBAL EXISTENCE; STATIONARY WAVES; SMOOTH SOLUTIONS; STABILITY;

D O I：

10.1016/j.jde.2022.01.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we are concerned with a quasi-linear hyperbolic-parabolic system of persistence and endogenous chemotaxis modelling vasculogenesis. Under some suitable structural assumption on the pressure function, we first predict and derive the system admits a nonlinear diffusion wave in R driven by the damping effect. Then we show that the solution of the concerned system will locally and asymptotically converge to this nonlinear diffusion wave if the wave strength is small. By using the time-weighted energy estimates, we further prove that the convergence rate of the nonlinear diffusion wave is algebraic. (c) 2022 Elsevier Inc. All rights reserved.

引用

页码：251 / 286

页数：36

共 54 条

[11] EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A QUASI-LINEAR HYPERBOLIC-PARABOLIC MODEL OF VASCULOGENESIS [J].

Di Russo, Cristiana ;

Sepe, Alice .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2013, 45 (02) :748-776

[12] Darcy's law and diffusion for a two-fluid Euler-Maxwell system with dissipation [J].

Duan, Renjun ;

Liu, Qingqing ;

Zhu, Changjiang .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2015, 25 (11) :2089-2151

[13] OPTIMAL DECAY RATES TO CONSERVATION LAWS WITH DIFFUSION-TYPE TERMS OF REGULARITY-GAIN AND REGULARITY-LOSS [J].

Duan, Renjun ;

Ruan, Lizhi ;

Zhu, Changjiang .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2012, 22 (07)

[14] Approximation of hyperbolic models for chemosensitive movement [J].

Filbet, F ;

Shu, CW .

SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2005, 27 (03) :850-872

[15] Percolation, morphogenesis, and Burgers dynamics in blood vessels formation [J].

Gamba, A ;

Ambrosi, D ;

Coniglio, A ;

de Candia, A ;

Di Talia, S ;

Giraudo, E ;

Serini, G ;

Preziosi, L ;

Bussolino, F .

PHYSICAL REVIEW LETTERS, 2003, 90 (11) :4

[16] Large time behavior of solutions of the bipolar hydrodynamical model for semiconductors [J].

Gasser, I ;

Hsiao, L ;

Li, HL .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 192 (02) :326-359

[17] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO EULER EQUATIONS WITH TIME-DEPENDENT DAMPING IN CRITICAL CASE [J].

Geng, Shifeng ;

Lin, Yanping ;

Mei, Ming .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2020, 52 (02) :1463-1488

[18] Nonlinear stability of phase transition steady states to a hyperbolic-parabolic system modeling vascular networks [J].

Hong, Guangyi ;

Peng, Hongyun ;

Wang, Zhi-An ;

Zhu, Changjiang .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2021, 103 (04) :1480-1514

[19] GLOBAL EXISTENCE AND BLOWUP OF SMOOTH SOLUTIONS OF 3-D POTENTIAL EQUATIONS WITH TIME-DEPENDENT DAMPING [J].

Hou, Fei ;

Witt, Ingo ;

Yin, Huicheng .

PACIFIC JOURNAL OF MATHEMATICS, 2018, 292 (02) :389-426

[20] On the global existence and blowup of smooth solutions to the multi-dimensional compressible Euler equations with time-depending damping [J].

Hou, Fei ;

Yin, Huicheng .

NONLINEARITY, 2017, 30 (06) :2485-2517

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