This paper is concerned with the existence and further properties of propagation speeds of transition fronts for bistable reaction-diffusion equations in exterior domains and in some domains with multiple cylindrical branches. In exterior domains we show that all transition fronts propagate with the same global mean speed, which turns out to be equal to the uniquely defined planar speed. In domains with multiple cylindrical branches, we show that the solutions emanating from some branches and propagating completely are transition fronts propagating with the unique planar speed. We also give some geometrical and scaling conditions on the domain, either exterior or with multiple cylindrical branches, which guarantee that any transition front has a global mean speed.

本文关注双稳态反应扩散方程在外部区域和某些具有多个圆柱分支的区域中过渡前沿传播速度的存在和进一步的性质。在外部域中，我们表明所有过渡前沿都以相同的全局平均速度传播，该速度等于唯一定义的平面速度。在具有多个圆柱形分支的区域中，我们证明了从某些分支发出并完全传播的解是以独特的平面速度传播的过渡前沿。我们还给出了在域上的几何和缩放条件，无论是外部的还是具有多个圆柱形分支的，都可以确保任何过渡前沿具有全局平均速度。