论文标题
被推到的前部转换：延续，速度尺度和隐藏的单调性
Pushed-to-pulled front transitions: continuation, speed scalings, and hidden monotonicity
论文作者
论文摘要
我们从独立于模型的角度分析和数值上分析和推动的前部之间的过渡。基于最小的概念假设，我们表明，从拉动前部的分支上推动前叉状，并具有有效的速度校正，在分叉参数中四次缩放。令人惊讶的是，我们发现，在这种一般环境中，没有关于比较原则的假设，拉动前部失去了稳定性，而当丢失了前沿中的单调性时，就会让位于推动的前部。我们的方法依赖于远场核心分解，这些分解识别正面前沿中明确的渐近分解。我们展示了如何直接实施理论构建，以产生有效的算法，这些算法确定扩展速度和分叉点在域大小中呈指数级误差。此处考虑的示例应用程序包括扩展的Fisher-KPP方程，一个渔民方程，负出租车与后勤人口增长，自催化反应和Lotka-Volterra模型结合使用。
We analyze the transition between pulled and pushed fronts both analytically and numerically from a model-independent perspective. Based on minimal conceptual assumptions, we show that pushed fronts bifurcate from a branch of pulled fronts with an effective speed correction that scales quadratically in the bifurcation parameter. Strikingly, we find that in this general context without assumptions on comparison principles, the pulled front loses stability and gives way to a pushed front when monotonicity in the leading edge is lost. Our methods rely on far-field core decompositions that identify explicitly asymptotics in the leading edge of the front. We show how the theoretical construction can be directly implemented to yield effective algorithms that determine spreading speeds and bifurcation points with exponentially small error in the domain size. Example applications considered here include an extended Fisher-KPP equation, a Fisher-Burgers equation, negative taxis in combination with logistic population growth, an autocatalytic reaction, and a Lotka-Volterra model.
