论文标题
负趋化性的速度行驶波
Speed-up of traveling waves by negative chemotaxis
论文作者
论文摘要
我们考虑在排斥趋化性的影响下，Fisher-KPP（FKPP）前部的波动速度，几乎完整地描绘了其对代表趋化性强度和长度尺度的参数的渐近依赖性。我们的研究基于与某些渐近方案中多孔培养基FKPP行驶波和双曲线FKPP-Keller-Segel行进波的收敛性。这样，它阐明了三个方程式之间的关系，这些方程式使每个方程都积累了强烈的兴趣。我们的证明涉及各种技术，从熵方法和振荡估算的衰减到对定性行为的一般描述到双曲线FKPP-keller-segel方程。对于后一个方程式，作为限制参数的一部分，我们在最小的行驶波速度上建立了明确的下限，并提供了将已知存在范围扩展到所有参数值的新构造。
We consider the traveling wave speed for Fisher-KPP (FKPP) fronts under the influence of repulsive chemotaxis and provide an almost complete picture of its asymptotic dependence on parameters representing the strength and length-scale of chemotaxis. Our study is based on the convergence to the porous medium FKPP traveling wave and a hyperbolic FKPP-Keller-Segel traveling wave in certain asymptotic regimes. In this way, it clarifies the relationship between three equations that have each garnered intense interest on their own. Our proofs involve a variety of techniques ranging from entropy methods and decay of oscillations estimates to a general description of the qualitative behavior to the hyperbolic FKPP-Keller-Segel equation. For this latter equation, we, as a part of our limiting arguments, establish an explicit lower bound on the minimal traveling wave speed and provide a new construction of traveling waves that extends the known existence range to all parameter values.
