Abstract:This paper is concerned with propagation phenomena of spatially periodic combustion reaction-diffusion equations in exterior domains. It is known that there is a pulsating front connecting 0 and 1 with positive speed in $\mathbb{R}^N$ for any direction $e\in\mathbb{S}^{N-1}$. We first prove that there exists an entire solution originating from a pulsating front in the exterior domain. Then, we prove that the entire solution propagates completely. Additionally, by constructing appropriate super- and sub-solutions, we establish that the entire solution is a transition front connecting 0 and 1, and that it is trapped between two translates of the pulsating front as $t\rightarrow +\infty$. Finally, under a suitable assumption, we show that the entire solution converges to the same pulsating front as $t\rightarrow +\infty$, as well as the uniqueness of such entire solutions.
From: Wei-Jie Sheng [view email]
[v1]
Wed, 24 Jun 2026 03:11:29 UTC (23 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。