Spatial patterns for reaction-diffusion systems with conditions described by inclusions

被引：0
|
作者：
Eisner J. [1 ]
Kučera M. [1 ]
机构：
[1] Mathematical Institute, Acad. of Sci. of the Czech Republic, 11567 Praha 1
来源：
Applications of Mathematics | 1997年 / 42卷 / 6期
关键词：
Bifurcation; Inclusions; Reaction-diffusion systems; Spatial patterns; Stationary solutions; Variational inequalities;
D O I：
10.1023/A:1022203129542
中图分类号：
学科分类号：
摘要：
We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.
引用
收藏
页码：421 / 449
页数：28
相关论文
共 50 条
  • [41] Asymptotic stability conditions for autonomous time-fractional reaction-diffusion systems
    Douaifia, Redouane
    AbdelmaleK, Salem
    Bendoukha, Samir
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 80
  • [42] Diffusion-driven instability in reaction-diffusion systems
    Wang, LC
    Li, MY
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 254 (01) : 138 - 153
  • [43] Global existence of solutions to reaction-diffusion systems without conditions on the nonlinearities growth
    Kouachi, Said
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2011, 34 (07) : 798 - 802
  • [44] A variational approach to bifurcation in reaction-diffusion systems with Signorini type boundary conditions
    Baltaev, Jamol I.
    Kucera, Milan
    Vaeth, Martin
    APPLICATIONS OF MATHEMATICS, 2012, 57 (02) : 143 - 165
  • [45] Time-delay-induced instabilities in reaction-diffusion systems
    Sen, Shrabani
    Ghosh, Pushpita
    Riaz, Syed Shahed
    Ray, Deb Shankar
    PHYSICAL REVIEW E, 2009, 80 (04):
  • [46] Finite-Time Spatial Sampled-Data Control for Reaction-Diffusion Systems
    Wu, Kai-Ning
    Wang, Zhen
    Wang, Yun-Zhu
    Cui, Zhiquan
    CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 2021, 40 (10) : 4833 - 4849
  • [47] How Spatial Heterogeneity Affects Transient Behavior in Reaction-Diffusion Systems for Ecological Interactions?
    Wang, Xiaoying
    Efendiev, Messoud
    Lutscher, Frithjof
    BULLETIN OF MATHEMATICAL BIOLOGY, 2019, 81 (10) : 3889 - 3917
  • [48] DYNAMICS OF LOCALIZED UNIMODAL PATTERNS IN REACTION-DIFFUSION SYSTEMS FOR CELL POLARIZATION BY EXTRACELLULAR SIGNALING
    Kuwamura, Masataka
    Seirin-Lee, Sungrim
    Ei, Shin-ichiro
    SIAM JOURNAL ON APPLIED MATHEMATICS, 2018, 78 (06) : 3238 - 3257
  • [49] Convergence of the finite difference scheme for a general class of the spatial segregation of reaction-diffusion systems
    Arakelyan, Avetik
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (12) : 4232 - 4240
  • [50] Hopping transport in hostile reaction-diffusion systems
    Missel, Andrew R.
    Dahmen, Karin A.
    PHYSICAL REVIEW E, 2009, 79 (02)
12345