论文标题
Lipschitz bistable或燃烧方面的特性及其应用
Lipschitz property of bistable or combustion fronts and its applications
论文作者
论文摘要
对于描述传播现象的一类反应扩散方程，我们证明，对于任何整个解决方案$ u $，级别集$ \ {u =λ\} $是时间方向的Lipschitz图，如果$λ$接近$ 1 $。在进一步的假设是，$ u $连接$ 0 $和$ 1 $，这表明所有级别的集合都是Lipschitz图。通过进行吹扫的分析，还给出了这些水平集的大规模运动定律，并给出了行驶波的最低速度的表征。
For a class of reaction-diffusion equations describing propagation phenomena, we prove that for any entire solution $u$, the level set $\{u=λ\}$ is a Lipschitz graph in the time direction if $λ$ is close to $1$. Under a further assumption that $u$ connects $0$ and $1$, it is shown that all level sets are Lipschitz graphs. By a blowing down analysis, the large scale motion law for these level sets and a characterization of the minimal speed for travelling waves are also given.
