有限域上反应扩散平流型出现的主分支和对称性
Principal bifurcations and symmetries in the emergence of reaction-diffusion-advection patterns on finite domains
摘要：
本文研究了具有一个扩散系数、微分平流和Danckwynn型（Robin）边界条件的反应-扩散-平流系统的斑图形成机理。模式选择需要映射域的共存和稳定的传播或固定的非均匀的解决方案，这对于一般情况下，远离不稳定的发作，进行使用空间动力学和数值延拓。选择由边界条件决定，边界条件可以保持或破坏模型的平移对称性。因此，我们解释的标准和性质的定常周期状态，如果系统是有界的，并表明传播的非线性波（包括孤立波）对平流对应于共存的家庭出现非线性从一个独特的振荡的Hopf不稳定性。因此，由此产生的模式选择是定性不同的对称有限波数图灵或霍普夫不稳定性。
英文摘要：
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of coexistence and stability of propagating or stationary nonuniform solutions, which for the general case of far from instability onsets, is conducted using spatial dynamics and numerical continuations. The selection is determined by the boundary conditions which either preserve or destroy the translational symmetry of the model. Accordingly, we explain the criterion and the properties of stationary periodic states if the system is bounded and show that propagation of nonlinear waves (including solitary) against the advective flow corresponds to coexisting family that emerges nonlinearly from a distinct oscillatory Hopf instability. Consequently, the resulting pattern selection is qualitatively different from the symmetric finite wavenumber Turing or Hopf instabilities.
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