论文标题
标量平衡法律中的稳定性和不稳定法律：前线和周期波
Stability and instability in scalar balance laws: fronts and periodic waves
论文作者
论文摘要
我们从光谱和非线性稳定性/不稳定性的角度从（分段）光滑的扰动下完成了标量平衡定律的全面分类。我们分析的一个惊人特征是阐明了特征点在确定线性算子光谱和非线性大型演化中涉及的相动态中的突出作用。对于一类方程式，我们的分析的结果是从巨大的熵行驶波到相对较小的稳定的熵行驶波的急剧减少。
We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is the elucidation of the prominent role of characteristic points in the determination of both the spectra of the linearized operators and the phase dynamics involved in the nonlinear large-time evolution. For a generic class of equations an upshot of our analysis is a dramatic reduction from a tremendously wide variety of entropic traveling waves to a relatively small range of stable entropic traveling waves.
