Localized and Expanding Entire Solutions of Reaction–Diffusion Equations

被引：0
作者：
F. Hamel
H. Ninomiya
机构：
[1] CNRS,Aix Marseille Univ
[2] Centrale Marseille,School of Interdisciplinary Mathematical Sciences
[3] I2M,undefined
[4] Meiji University,undefined
来源：
Journal of Dynamics and Differential Equations | 2022年 / 34卷
关键词：
Reaction–diffusion equations; Entire solutions; Extinction; Propagation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper is concerned with the spatio-temporal dynamics of nonnegative bounded entire solutions of some reaction–diffusion equations in RN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^N$$\end{document} 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.
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页码：2937 / 2974
页数：37
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