论文标题
树木上双态微分方程的繁殖逆转
Propagation reversal for bistable differential equations on trees
论文作者
论文摘要
我们研究了无限$ k $ are树的双态微分方程的行动波解决方案。这些图概括了古典方形无限晶格的概念，我们的结果补充了$ \ mathbb {z} $上的Bistable晶格方程的概念。使用比较原理和明确的下层解决方案，我们表明波 - 溶解是针对小扩散参数固定的。在增加扩散后，波浪开始以非零速度的速度传播，该方向取决于引起的参数。但是，一旦扩散足够强大，波浪就会向上沿单个方向传播，而不论引起的参数如何。特别是，我们的结果表明，扩散参数的变化可能导致传播方向的逆转。
We study traveling wave solutions to bistable differential equations on infinite $k$-ary trees. These graphs generalize the notion of classical square infinite lattices and our results complement those for bistable lattice equations on $\mathbb{Z}$. Using comparison principles and explicit lower and upper solutions, we show that wave-solutions are pinned for small diffusion parameters. Upon increasing the diffusion, the wave starts to travel with non-zero speed, in a direction that depends on the detuning parameter. However, once the diffusion is sufficiently strong, the wave propagates in a single direction up the tree irrespective of the detuning parameter. In particular, our results imply that changes to the diffusion parameter can lead to a reversal of the propagation direction.
