Uniqueness and stability of forced waves for the Fisher-KPP equation in a shifting environment ☆

被引：0

作者：

Guo, Jong-Shenq ^{[1
]}

Guo, Karen ^{[2
]}

Shimojo, Masahiko ^{[3
]}

机构：

[1] Tamkang Univ, Dept Math, New Taipei City 251301, Taiwan

[2] Providence Univ, Dept Data Sci & Big Data Analyt, Taichung, Taiwan

[3] Tokyo Metropolitan Univ, Dept Math Sci, Hachioji, Tokyo 1920397, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2024年 / 247卷

关键词：

Forced wave; Shifting speed; Saturation; Stability; Uniqueness; REACTION-DIFFUSION EQUATIONS; PRINCIPAL EIGENVALUE; POPULATION-DYNAMICS; ELLIPTIC-OPERATORS; CLIMATE-CHANGE; MODEL;

D O I：

10.1016/j.na.2024.113607

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the existence, uniqueness and stability of forced waves for the Fisher-KPP equation in a shifting environment without imposing the monotonicity condition on the shifting intrinsic growth term. First, the existence of forced waves for some range of shifting speeds is proved. Then we prove the uniqueness of saturation forced waves. Moreover, a new method is introduced to derive the non-existence of forced waves. Finally, we derive the stability of forced waves under certain perturbation of a class of initial data.

引用

页数：10

共 25 条

[1] Berestycki H, 2006, J EUR MATH SOC, V8, P195
[2] THE PRINCIPAL EIGENVALUE AND MAXIMUM PRINCIPLE FOR 2ND-ORDER ELLIPTIC-OPERATORS IN GENERAL DOMAINS
BERESTYCKI, H
NIRENBERG, L
VARADHAN, SRS
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1994, 47 (01) : 47 - 92
[3] Berestycki H, 2008, DISCRETE CONT DYN-A, V21, P41
[4] Liouville-type results for semilinear elliptic equations in unbounded domains
Berestycki, Henri
Hamel, Francois
Rossi, Luca
[J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2007, 186 (03) : 469 - 507
[5] Forced waves of the Fisher-KPP equation in a shifting environment
Berestycki, Henri
Fang, Jian
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (03) : 2157 - 2183
[6] Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains
Berestycki, Henri
Rossi, Luca
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2015, 68 (06) : 1014 - 1065
[7] Can climate change lead to gap formation?
Berestycki, Henri
Desvillettes, Laurent
Diekmann, Odo
[J]. ECOLOGICAL COMPLEXITY, 2014, 20 : 264 - 270
[8] REACTION-DIFFUSION EQUATIONS FOR POPULATION DYNAMICS WITH FORCED SPEED II - CYLINDRICAL-TYPE DOMAINS
Berestycki, Henri
Rossi, Luca
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 25 (01) : 19 - 61
[9] Forced waves of a three species predator-prey system in a shifting environment
Choi, Wonhyung
Guo, Jong-Shenq
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 514 (01)
[10] Persistence of species in a predator-prey system with climate change and either nonlocal or local dispersal
Choi, Wonhyung
Giletti, Thomas
Guo, Jong-Shenq
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 302 : 807 - 853

← 1 2 3 →