论文标题
反应扩散模型中的冲击悬挂的行进波，非线性前向前向扩散
Shock-fronted travelling waves in a reaction-diffusion model with nonlinear forward-backward-forward diffusion
论文作者
论文摘要
反应扩散方程（RDE）通常被得出为基于晶格的离散模型的连续限制。最近，一个离散的模型允许运动，增殖和死亡的速率取决于是否已提出了隔离的代理，并且这种方法给出了各种RDE，其中扩散项为凸并且可能变为负（Johnston等人，Sci。Ep。7，2017），即前向前进的扩散。数值模拟表明，当反应项包含Allee效应时，这些RDE支持冲击的行进波。在这项工作中，我们通过将RDE嵌入更大类别的高阶偏微分方程（PDES）中分析冲击框的行进波来形式化这些初步的数值观察。随后，我们使用几何奇异扰动理论来研究这种较大的方程式，并证明了这些冲击悬挂的行进波的存在。最值得注意的是，我们表明，不同的嵌入产生具有不同特性的冲击式流动波。
Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, proliferation and death to depend upon whether the agents are isolated has been proposed, and this approach gives various RDEs where the diffusion term is convex and can become negative (Johnston et al., Sci. Rep. 7, 2017), i.e. forward-backward-forward diffusion. Numerical simulations suggest these RDEs support shock-fronted travelling waves when the reaction term includes an Allee effect. In this work we formalise these preliminary numerical observations by analysing the shock-fronted travelling waves through embedding the RDE into a larger class of higher order partial differential equations (PDEs). Subsequently, we use geometric singular perturbation theory to study this larger class of equations and prove the existence of these shock-fronted travelling waves. Most notable, we show that different embeddings yield shock-fronted travelling waves with different properties.
