一般局部甘蔗蟾蜍模型的超线性传播
Super-linear propagation for a general, local cane toads model
摘要：
我们调查了一个一般的，本地版本的甘蔗蟾蜍方程，该模型的传播人口结构的无界运动。我们使用Evans和Souganwei在[Indiana Univ. Math. J.，1989]，以获得在线性化方程和几何前沿方程方面的传播的表征。特别是，我们减少了任务的理解的精确位置的前一个大类的方程分析一类小得多的Hamilton-Jacobi方程。然后，我们能够给出一个明确的公式，在物理空间中的前位置。我们的方法的一个优点是，我们不使用人口传播的明确轨迹，这是以前工作的基础。我们的结果允许在运动的大振荡。
英文摘要：
We investigate a general, local version of the cane toads equation, which models the spread of a population structured by unbounded motility. We use the thin-front limit approach of Evans and Souganidis in [Indiana Univ. Math. J., 1989] to obtain a characterization of the propagation in terms of both the linearized equation and a geometric front equation. In particular, we reduce the task of understanding the precise location of the front for a large class of equations to analyzing a much smaller class of Hamilton-Jacobi equations. We are then able to give an explicit formula for the front location in physical space. One advantage of our approach is that we do not use the explicit trajectories along which the population spreads, which was a basis of previous work. Our result allows for large oscillations in the motility.
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