反应扩散方程的局部解和扩张整体解
Localized and Expanding Entire Solutions of Reaction-Diffusion Equations
摘要：
本文研究了在任意空间维N上，R N上一类反应扩散方程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。
英文摘要：
This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction-diffusion equations in R N in any space dimension N. 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
