A DYNAMICAL SYSTEM FOR A NONLOCAL PARABOLIC EQUATION WITH EXPONENTIAL NONLINEARITY

被引：1
|
作者：
Miyasita, Tosiya
机构：
[1] 250-201 Imamichi-cho, Kyoto
来源：
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2015年 / 45卷 / 06期
关键词：
Nonlocal; Morse index; Lyapunov function; exponential attractor; squeezing property; 2-DIMENSIONAL EULER EQUATIONS; STATIONARY FLOWS; BLOW; INEQUALITY; SYMMETRY;
D O I：
10.1216/RMJ-2015-45-6-1897
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider a nonlocal parabolic and the corresponding elliptic equation with exponential nonlinearity. At first, we study the set of a stationary solution and compute its Morse index. Next, we obtain the time-global solution in the use of the Lyapunov function and define the dynamical system. Finally, we construct an exponential attractor by a squeezing property.
引用
收藏
页码：1897 / 1917
页数：21
相关论文
共 50 条
  • [11] Optical solitons for weakly nonlocal Schrodinger equation with parabolic law nonlinearity and external potential
    Akinyemi, Lanre
    Senol, Mehmet
    Mirzazadeh, Mohammad
    Eslami, Mostafa
    OPTIK, 2021, 230
  • [12] Blow-up and non-extinction for a nonlocal parabolic equation with logarithmic nonlinearity
    Lijun Yan
    Zuodong Yang
    Boundary Value Problems, 2018
  • [13] Blow-up and non-extinction for a nonlocal parabolic equation with logarithmic nonlinearity
    Yan, Lijun
    Yang, Zuodong
    BOUNDARY VALUE PROBLEMS, 2018,
  • [14] Bright and dark solitons of a weakly nonlocal Schrodinger equation involving the parabolic law nonlinearity
    Hosseini, Kamyar
    Salahshour, Soheil
    Mirzazadeh, Mohammad
    OPTIK, 2021, 227
  • [15] SCHRODINGER EQUATION WITH EXPONENTIAL NONLINEARITY
    SHEERIN, JP
    ONG, RSB
    PHYSICS LETTERS A, 1977, 63 (03) : 279 - 280
  • [16] Propagation dynamics in a nonlocal delayed lattice dynamical system with bistable nonlinearity
    Xu, Zhaoquan
    Wu, Chufen
    JOURNAL OF MATHEMATICAL PHYSICS, 2022, 63 (04)
  • [17] GLOBAL ATTRACTOR FOR A SEMILINEAR STRONGLY DEGENERATE PARABOLIC EQUATION WITH EXPONENTIAL NONLINEARITY IN UNBOUNDED DOMAINS
    Nguyen Xuan Tu
    COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2022, 37 (02): : 423 - 443
  • [18] A parabolic equation with nonlocal conditions
    Sil'chenko Yu.T.
    Journal of Mathematical Sciences, 2008, 149 (6) : 1701 - 1707
  • [19] Nonlocal Kirchhoff Problems with Singular Exponential Nonlinearity
    Xiang Mingqi
    Radulescu, Vicentiu D.
    Zhang, Binlin
    APPLIED MATHEMATICS AND OPTIMIZATION, 2021, 84 (01): : 915 - 954
  • [20] Nonlocal Kirchhoff Problems with Singular Exponential Nonlinearity
    Xiang Mingqi
    Vicenţiu D. Rădulescu
    Binlin Zhang
    Applied Mathematics & Optimization, 2021, 84 : 915 - 954
12345