Topological stability of Chafee-Infante equations under Lipschitz perturbations of the domain and equation

被引：4
|
作者：
Lee, Jihoon [1 ]
Nguyen, Ngocthach [2 ]
机构：
[1] Chonnam Natl Univ, Dept Math, Gwangju 61186, South Korea
[2] Chungnam Natl Univ, Dept Math, Daejeon 34134, South Korea
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 517卷 / 02期
关键词：
Chafee-Infante equation; Geometric equivalence; Topological stability; Global attractor; Lipschitz perturbation; L-Morse-Smale; NONLINEAR BOUNDARY-CONDITIONS; REACTION-DIFFUSION EQUATIONS; ATTRACTORS; CONTINUITY;
D O I：
10.1016/j.jmaa.2022.126628
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the dynamics of Chafee-Infante equations under Lipschitz perturbations of the domain and equation. First, we describe the geometric equivalence between the global attractor A(0) of the Chafee-Infante equation and the global attractors A(eta )of the perturbed systems. Moreover, we show that the equation is topologically stable on its global attractor in the Gromov-Hausdorff sense. (C) 2022 Elsevier Inc. All rights reserved.
引用
收藏
页数：28
相关论文
共 50 条
  • [1] Lipschitz perturbations of the Chafee-Infante equation
    Pires, Leonardo
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 519 (01)
  • [2] TOPOLOGICAL EQUIVALENCE OF GLOBAL ATTRACTORS FOR LIPSCHITZ PERTURBATIONS OF THE CHAFEE-INFANTE EQUATION
    Bortolan, Matheus C.
    Pires, Leonardo
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2023, 28 (08): : 4519 - 4531
  • [3] The Stochastic Chafee-Infante Equation
    Debussche, Arnaud
    Hoegele, Michael
    Imkeller, Peter
    DYNAMICS OF NONLINEAR REACTION-DIFFUSION EQUATIONS WITH SMALL LEVY NOISE, 2013, 2085 : 45 - 68
  • [4] The Fine Dynamics of the Chafee-Infante Equation
    Debussche, Arnaud
    Hoegele, Michael
    Imkeller, Peter
    DYNAMICS OF NONLINEAR REACTION-DIFFUSION EQUATIONS WITH SMALL LEVY NOISE, 2013, 2085 : 11 - 43
  • [5] ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE CHAFEE-INFANTE EQUATION
    黄浩川
    黄锐
    ActaMathematicaScientia, 2020, 40 (02) : 425 - 441
  • [6] Asymptotic Behavior of Solutions for the Chafee-Infante Equation
    Huang, Haochuan
    Huang, Rui
    ACTA MATHEMATICA SCIENTIA, 2020, 40 (02) : 425 - 441
  • [7] Asymptotic Behavior of Solutions for the Chafee-Infante Equation
    Haochuan Huang
    Rui Huang
    Acta Mathematica Scientia, 2020, 40 : 425 - 441
  • [8] Sign changing periodic solutions for the Chafee-Infante equation
    Huang, Haochuan
    Huang, Rui
    APPLICABLE ANALYSIS, 2018, 97 (13) : 2313 - 2331
  • [9] On the pitchfork bifurcation for the Chafee-Infante equation with additive noise
    Blumenthal, Alex
    Engel, Maximilian
    Neamtu, Alexandra
    PROBABILITY THEORY AND RELATED FIELDS, 2023, 187 (3-4) : 603 - 627
  • [10] The effect of noise on the Chafee-Infante equation: A nonlinear case study
    Caraballo, Tomas
    Crauel, Hans
    Langa, Jose A.
    Robinson, James C.
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (02) : 373 - 382
12345