论文标题
扩展的Fisher-KPP方程中关键阵线的光谱稳定性
Spectral stability of the critical front in the extended Fisher-KPP equation
论文作者
论文摘要
我们重新审视了扩展的Fisher-KPP方程中临界方程的存在和稳定性，从而完善了Rottschäfer和Wayne [28]的早期结果，它们在不识别精确的衰减率的情况下建立了前沿的稳定性。我们验证了前部的频谱稳定：虽然必需的频谱触及原点的假想轴，但没有不稳定的特征值，也没有嵌入在原点的基本频谱中的特征值（或共振）。与Avery和Scheel [3]的最新工作一起，这意味着与先前在经典的Fisher-KPP方程中获得的临界界面的非线性稳定性具有尖锐的$ T^{ - 3/2} $衰减率。主要挑战是将扩展的Fisher-KPP方程中的奇异扰动正规化，并跟踪基本频谱附近的特征值，我们通过功能分析方法克服了这些困难。
We revisit the existence and stability of the critical front in the extended Fisher-KPP equation, refining earlier results of Rottschäfer and Wayne [28] which establish stability of fronts without identifying a precise decay rate. We verify that the front is marginally spectrally stable: while the essential spectrum touches the imaginary axis at the origin, there are no unstable eigenvalues and no eigenvalue (or resonance) embedded in the essential spectrum at the origin. Together with the recent work of Avery and Scheel [3], this implies nonlinear stability of the critical front with sharp $t^{-3/2}$ decay rate, as previously obtained in the classical Fisher-KPP equation. The main challenges are to regularize the singular perturbation in the extended Fisher-KPP equation and to track eigenvalues near the essential spectrum, and we overcome these difficulties with functional analytic methods.
