Localized and Expanding Entire Solutions of Reaction?Diffusion Equations
Localized and Expanding Entire Solutions of Reaction?Diffusion Equations
复制标题
反应扩散方程的定域和扩展全解
DOI：
10.1007/s10884-020-09936-2
复制
发表时间：
2021
影响因子：
1.3
通讯作者：
Ninomiya H.
中科院分区：
文献类型：
--
作者：
Hamel F.;Ninomiya H.
研究了一类反应扩散方程在任意空间维N上的非负有界整体解的时空动力学性质。假设解在过去是局部化的。在一定的反应项条件下，证明了解是与时间无关的或不同定态之间的异宿联系。此外，它们要么在时间上均匀地局部化，要么收敛到一个恒定的稳态并在很长时间内扩散。然后将这一结果应用于某些特定的双稳态反应。
This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction–diffusion equations inin any space dimensionN. The solutions are assumed to be localized in the past. Under certain conditions on the reaction term, the solutions are then proved to be time-independent or heteroclinic connections between different steady states. Furthermore, either they are localized uniformly in time, or they converge to a constant steady state and spread at large time. This result is then applied to some specific bistable-type reactions.