论文标题
在非局部正则化下，冲击悬挂的行进波的非线性稳定性
Nonlinear stability of shock-fronted travelling waves under nonlocal regularization
论文作者
论文摘要
我们确定在反应非线性扩散PDE中产生的冲击式流动波的非线性稳定性，但要经过四阶空间衍生术语，乘以模型{\ it nonlocal正则化}的小参数$ \ varepsilon $乘以。由作者最近对粘性放松下的冲击悬挂流动波进行的稳定性分析的动机，我们的数值分析是通过观察到的，即线性化操作员对相关特征值问题的快速分解。特别是，我们观察到复杂的四维特征值问题的惊人减少为{\ IT}沿慢速歧管定义的一维问题。即，当$ \ varepsilon = 0 $统治线性化运算符的点频谱时，当$ 0 <\ varepsilon \ ll 1 $时，定义的慢速特征值在电击波浪的尾部附近定义。
We determine the nonlinear stability of shock-fronted travelling waves arising in a reaction-nonlinear diffusion PDE, subject to a fourth-order spatial derivative term multiplied by a small parameter $\varepsilon$ that models {\it nonlocal regularization}. Motivated by the authors' recent stability analysis of shock-fronted travelling waves under viscous relaxation, our numerical analysis is guided by the observation that there is a fast-slow decomposition of the associated eigenvalue problem for the linearised operator. In particular, we observe an astonishing reduction of the complex four-dimensional eigenvalue problem into a {\it real} one-dimensional problem defined along the slow manifolds; i.e. slow eigenvalues defined near the tails of the shock-fronted wave for $\varepsilon = 0$ govern the point spectrum of the linearised operator when $0 < \varepsilon \ll 1$.
