论文标题
FKPP爆炸系统中的行进波速度
The speed of traveling waves in a FKPP-Burgers system
论文作者
论文摘要
我们考虑基于Fisher-KPP和汉堡方程的耦合反应 - 添加扩散系统。这些方程是一种用于反应流体的模型的一维版本，其中产生的密度差异诱导流体升级的浮力。我们通过流动波解决方案的镜头研究该系统中的前繁殖。我们能够根据耦合常数$ρ$大还是小，可以显示两种完全不同的行为。首先，证明存在阈值$ρ_0$，根据该阈值，对流对行驶波的速度没有影响（尽管对流为非零）。其次，当$ρ$很大时，波速必须至少为$ \ MATHCAL {O}（ρ^{1/3}）$。这些结果在一起使得随着$ρ$的增加，从拉力到推动波的过渡。由于该模型和类似模型涉及复杂的动力学，因此这是文献中关于耦合对波动波解决方案效果的第一个精确结果之一。我们在分析处理中使用了普通和部分微分方程方法的混合，并通过数值处理来补充它，该方法采用新创建的方法来了解波速的行为。最后，提出了各种猜想和开放问题。
We consider a coupled reaction-advection-diffusion system based on the Fisher-KPP and Burgers equations. These equations serve as a one-dimensional version of a model for a reacting fluid in which the arising density differences induce a buoyancy force advecting the fluid. We study front propagation in this system through the lens of traveling waves solutions. We are able to show two quite different behaviors depending on whether the coupling constant $ρ$ is large or small. First, it is proved that there is a threshold $ρ_0$ under which the advection has no effect on the speed of traveling waves (although the advection is nonzero). Second, when $ρ$ is large, wave speeds must be at least $\mathcal{O}(ρ^{1/3})$. These results together give that there is a transition from pulled to pushed waves as $ρ$ increases. Because of the complex dynamics involved in this and similar models, this is one of the first precise results in the literature on the effect of the coupling on the traveling wave solution. We use a mix of ordinary and partial differential equation methods in our analytical treatment, and we supplement this with a numerical treatment featuring newly created methods to understand the behavior of the wave speeds. Finally, various conjectures and open problems are formulated.
