The asymptotic behaviour of the heat equation in a sheared unbounded strip

被引：0
|
作者：
Tichy, Michal [1 ]
机构：
[1] Czech Tech Univ, Fac Nucl Sci & Phys Engn, Dept Math, Prague, Czech Republic
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2021年 / 297卷
关键词：
Dirichlet Laplacian; Hardy inequality; Subcriticality; Heat equation; Large-time behaviour of solutions; Sheared strip; HARDY INEQUALITY;
D O I：
10.1016/j.jde.2021.06.026
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the geometric deformation of shearing yields an improved decay rate for the heat semigroup associated with the Dirichlet Laplacian in an unbounded strip. The proof is based on the Hardy inequality due to the shearing established in [2] and the method of self-similar variables and weighted Sobolev spaces for the heat equation. (c) 2021 Elsevier Inc. All rights reserved.
引用
收藏
页码：575 / 600
页数：26
相关论文
共 50 条
  • [31] Asymptotic behaviour and attractors for degenerate parabolic equations on unbounded domains
    Feireisl, E
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1996, 26 (09) : 1535 - 1546
  • [32] Asymptotic behaviour for the Kirchhoff equation.
    Ghisi, M
    ANNALI DI MATEMATICA PURA ED APPLICATA, 1996, 171 : 293 - 312
  • [33] Asymptotic behaviour for a semilinear nonlocal equation
    Pazoto, Ademir F.
    Rossi, Julio D.
    ASYMPTOTIC ANALYSIS, 2007, 52 (1-2) : 143 - 155
  • [34] Asymptotic behaviour of a generalized Burgers' equation
    Reyes, G
    Vazquez, JL
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1999, 78 (06): : 633 - 666
  • [35] On the asymptotic behaviour of the solutions to the replicator equation
    Karev, Georgy P.
    Novozhilov, Artem S.
    Berezovskaya, Faina S.
    MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA, 2011, 28 (02): : 89 - 110
  • [36] An inverse problem for the heat equation in an unbounded guide
    Cardoulis, Laure
    Cristofol, Michel
    APPLIED MATHEMATICS LETTERS, 2016, 62 : 63 - 68
  • [37] Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type
    Luis Vazquez, Juan
    JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2014, 16 (04) : 769 - 803
  • [38] Asymptotic Behaviour in a Certain Nonlinearly Perturbed Heat Equation: Non Periodic Perturbation Case
    Ramos, Carlos
    Santos, Ana
    Vinagre, Sandra
    DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH APPLICATIONS, 2018, 230 : 581 - 593
  • [39] ON THE ASYMPTOTIC-BEHAVIOR OF SOLUTIONS OF A PARABOLIC EQUATION IN A STRIP
    GUSAROV, AL
    DOKLADY AKADEMII NAUK SSSR, 1981, 257 (01): : 18 - 21
  • [40] Asymptotic behaviour of the Bessel heat kernels
    Kamil Bogus
    Mathematische Zeitschrift, 2019, 293 : 1601 - 1621
12345