抽象发展方程的强迫平移破缺：行波阻塞的组织中心
Forced translational symmetry-breaking for abstract evolution equations: the organizing center for blocking of travelling waves
摘要：
我们考虑巴拿赫空间X上的两个参数微分方程族，其中参数c和$ε$使得：（1）当$ε=0$时，微分方程在作用于X的一维平移群SE（1）的作用下是对称的，而当$ε\neq 0$时，这种平移对称性被破坏，（2）当$ε=0$时，对称微分方程允许由漂移速度c参数化的相对平衡（行波）的平滑族，其中$c=0$对应于稳态。在对微分方程和巴拿赫空间X的一定假设下，利用Sandstede，Scheel和Wulff的中心流形定理，研究了扰动破缺对上述相对平衡点族的影响.特别是，我们表明，通常被称为传播失败，或波阻塞的现象发生在一个圆锥体中的$(c,ε)$参数空间，从点$(c,ε)=(0,0)$发出。我们还讨论了如何我们的方法可以适应扰动的参数无关的微分方程（如费舍尔-KPP）承认家庭的相对平衡参数化漂移速度。
英文摘要：
We consider two parameter families of differential equations on a Banach space X, where the parameters c and $ε$ are such that: (1) when $ε=0$, the differential equations are symmetric under the action of the group of one-dimensional translations SE(1) acting on X, whereas when $ε\neq 0$, this translation symmetry is broken, (2) when $ε=0$, the symmetric differential equations admit a smooth family of relative equilibria (travelling waves) parametrized by the drift speed c, with $c=0$ corresponding to steady-states. Under certain hypotheses on the differential equations and on the Banach space X, we use the center manifold theorem of Sandstede, Scheel and Wulff to study the effects of the symmetry-breaking perturbation on the above family of relative equilibria. In particular, we show that the phenomenon commonly referred to as propagation failure, or wave blocking occurs in a cone in the $(c,ε)$ parameter space which emanates from the point $(c,ε)=(0,0)$. We also discuss how our methods can be adapted to perturbations of parameter-independent differential equations (such as the Fisher-KPP) which admit families of relative equilibria parametrized by drift speed.
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