TRANSITION FRONTS FOR THE FISHER-KPP EQUATION

被引：28

作者：

Hamel, Francois ^{[1
]}

Rossi, Luca ^{[2
,3
]}

机构：

[1] Aix Marseille Univ, CNRS, Cent Marseille, Inst Math Marseille,UMR 7373, F-13453 Marseille, France

[2] Univ Padua, Dipartimento Matemat P&A, Via Trieste 63, I-35121 Padua, Italy

[3] CNRS, UMR 8557, Ctr Anal & Math Sociales, F-75244 Paris 13, France

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 368卷 / 12期

基金：

欧洲研究理事会;

关键词：

GENERALIZED TRAVELING-WAVES; SPREADING SPEEDS; VARIATIONAL PRINCIPLE; DIFFUSION; PROPAGATION; CONVERGENCE; EXISTENCE;

D O I：

10.1090/tran/6609

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is concerned with transition fronts for reaction-diffusion equations of the Fisher-KPP type. Basic examples of transition fronts connecting the unstable steady state to the stable one are the standard traveling fronts, but the class of transition fronts is much larger and the dynamics of the solutions of such equations is very rich. In the paper, we describe the class of transition fronts and we study their qualitative dynamical properties. In particular, we characterize the set of their admissible asymptotic past and future speeds and their asymptotic profiles and we show that the transition fronts can only accelerate. We also classify the transition fronts in the class of measurable superpositions of standard traveling fronts.

引用

页码：8675 / 8713

页数：39

共 50 条

[21] SHARP INTERFACE LIMIT OF THE FISHER-KPP EQUATION [J].

Alfaro, Matthieu ;

Ducrot, Arnaud .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2012, 11 (01) :1-18

[22] Ahead of the Fisher-KPP front [J].

Brunet, Eric .

NONLINEARITY, 2023, 36 (10) :5541-5567

[23] Propagation in a Fisher-KPP equation with non-local advection [J].

Hamel, Francois ;

Henderson, Christopher .

JOURNAL OF FUNCTIONAL ANALYSIS, 2020, 278 (07)

[24] Warning signs for wave speed transitions of noisy Fisher-KPP invasion fronts [J].

Kuehn, Christian .

THEORETICAL ECOLOGY, 2013, 6 (03) :295-308

[25] On bounded positive stationary solutions for a nonlocal Fisher-KPP equation [J].

Achleitner, Franz ;

Kuehn, Christian .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 112 :15-29

[26] The Stefan problem for the Fisher-KPP equation with unbounded initial range [J].

Ding, Weiwei ;

Du, Yihong ;

Guo, Zongming .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (02)

[27] BOUNDS ON THE CRITICAL TIMES FOR THE GENERAL FISHER-KPP EQUATION [J].

Rodrigo, Marianito R. .

ANZIAM JOURNAL, 2021, 63 (04) :448-468

[28] Spreading Speed in the Fisher-KPP Equation with Nonlocal Delay [J].

Ge Tian ;

Haoyu Wang ;

Zhicheng Wang .

Acta Mathematica Scientia, 2021, 41 :875-886

[29] Spreading Speed in the Fisher-KPP Equation with Nonlocal Delay [J].

Tian, Ge ;

Wang, Haoyu ;

Wang, Zhicheng .

ACTA MATHEMATICA SCIENTIA, 2021, 41 (03) :875-886

[30] Stability of traveling waves of the nonlocal Fisher-KPP equation [J].

Tian, Ge ;

Wang, Zhi-Cheng ;

Zhang, Guo-Bao .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2021, 211

← 1 2 3 4 5 →