论文标题
标量粘性平衡法的周期性波的轨道不稳定
Orbital instability of periodic waves for scalar viscous balance laws
论文作者
论文摘要
本文的目的是证明，对于一类称为标量粘性平衡定律的大量非线性进化方程，周期性波动波解决方案的光谱（线性）不稳定性意味着它们在适当的周期性Sobolev空间中的轨道（非线性）不稳定。该分析基于适当的理论，数据解决图的平滑度以及在非线性迭代下平衡不稳定的抽象结果。由此产生的不稳定性标准应用于两个周期性波的家族。第一个家庭由有限基本时期的小幅度波组成，这些波浪来自当地的霍夫夫分叉，围绕速度的临界值。第二个家庭包括任意较大的周期波，这是由同型（全球）分叉产生的，当它们的基本周期倾向于无限时，倾向于限制行进脉冲。对于两个家庭，该标准用于在周期性Sobolev空间中与波浪基本时期相同的周期性Sobolev空间中的非线性粘性平衡定律的流动结论。
The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of periodic traveling wave solutions implies their orbital (nonlinear) instability in appropriate periodic Sobolev spaces. The analysis is based on the well-posedness theory, the smoothness of the data-solution map, and an abstract result of instability of equilibria under nonlinear iterations. The resulting instability criterion is applied to two families of periodic waves. The first family consists of small amplitude waves with finite fundamental period which emerge from a local Hopf bifurcation around a critical value of the velocity. The second family comprises arbitrarily large period waves which arise from a homoclinic (global) bifurcation and tend to a limiting traveling pulse when their fundamental period tends to infinity. In the case of both families, the criterion is applied to conclude their orbital instability under the flow of the nonlinear viscous balance law in periodic Sobolev spaces with same period as the fundamental period of the wave.
