论文标题
临界拉的正面的渐近稳定性通过基本光谱附近的分解扩展
Asymptotic stability of critical pulled fronts via resolvent expansions near the essential spectrum
论文作者
论文摘要
我们研究了在实际秩序的真实行中，在标量抛物线方程中拉动前线的非线性稳定性，在对前沿的存在和光谱稳定性的概念假设下。在这种一般环境中，我们建立了对正面扰动的敏锐代数衰减率和时间渐近。其中一些结果是Fisher-KPP方程的特定示例已知的，因此我们的结果可以被视为建立了该简单模型的某些方面的普遍性。我们还精确地描述了扰动对前部的空间定位如何影响渐近稳定性所具有的整个本地化范围内的时间衰减率。从技术上讲，我们的方法是基于对线性化问题的分解运算符的详细研究，通过该研究，我们通过该研究获得了直接非线性分析的清晰线性时间衰减估计值。
We study nonlinear stability of pulled fronts in scalar parabolic equations on the real line of arbitrary order, under conceptual assumptions on existence and spectral stability of fronts. In this general setting, we establish sharp algebraic decay rates and temporal asymptotics of perturbations to the front. Some of these results are known for the specific example of the Fisher-KPP equation, and our results can thus be viewed as establishing universality of some aspects of this simple model. We also give a precise description of how the spatial localization of perturbations to the front affects the temporal decay rate, across the full range of localizations for which asymptotic stability holds. Technically, our approach is based on a detailed study of the resolvent operator for the linearized problem, through which we obtain sharp linear time decay estimates that allow for a direct nonlinear analysis.
