Remarks on some dissipative sine-Gordon equations

被引：7
|
作者：
Goubet, O. [1 ]
机构：
[1] Univ Picardie Jules Verne, CNRS, LAMFA, UMR 7352, Amiens, France
来源：
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2020年 / 65卷 / 08期
关键词：
Sine-Gordon equations; attractors; solutions of elliptic equations; CONVERGENCE; ATTRACTORS;
D O I：
10.1080/17476933.2019.1597069
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this short note, we discuss some results concerning the long-time behaviour of solutions to dissipative sine-Gordon equation in a bounded domain of . We first prove that without forcing term and under some assumptions on the domain then the global attractor reduces to . We then rewrite the sine-Gordon equation as a Schrodinger equation with smoothing; this allows us to provide another proof for the so-called asymptotical smoothing effect for this dissipative wave equation.
引用
收藏
页码：1336 / 1342
页数：7
相关论文
共 50 条
  • [41] Bidifferential Calculus, Matrix SIT and Sine-Gordon Equations
    Dimakis, A.
    Kanning, N.
    Mueller-Hoissen, F.
    ACTA POLYTECHNICA, 2011, 51 (02) : 33 - 37
  • [42] Boundary feedback stabilization of coupled sine-Gordon equations
    Kobayashi, Toshihiro
    Sakamoto, Tetsuzo
    IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 2006, 23 (04) : 475 - 484
  • [43] Sine-Gordon on a wormhole
    Bizon, Piotr
    Dunajski, Maciej
    Kahl, Michel
    Kowalczyk, Michel
    NONLINEARITY, 2021, 34 (08) : 5520 - 5537
  • [44] Sine-Gordon revisited
    Dimock, J
    Hurd, TR
    ANNALES HENRI POINCARE, 2000, 1 (03): : 499 - 541
  • [45] Sine-Gordon Revisited
    J. Dimock
    T.R. Hurd
    Annales Henri Poincaré, 2000, 1 : 499 - 541
  • [46] The sine-Gordon wobble
    Kälbermann, G
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2004, 37 (48): : 11603 - 11612
  • [47] Numerical solutions of some stochastic hyperbolic wave equations including sine-Gordon equation
    Tuckwell, Henry C.
    WAVE MOTION, 2016, 65 : 130 - 146
  • [48] QUANTUM-THERMAL CROSSOVER IN THE DISSIPATIVE DYNAMICS OF THE SINE-GORDON MODEL
    HIDA, K
    ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 1985, 61 (02): : 223 - 229
  • [49] SINE-GORDON EQUATION
    HEYERHOFF, M
    MATHEMATICAL INTELLIGENCER, 1995, 17 (03): : 4 - &
  • [50] SINE-GORDON EQUATION
    RUBINSTE.J
    JOURNAL OF MATHEMATICAL PHYSICS, 1970, 11 (01) : 258 - +
12345