非均匀介质中离散Fisher-KPP方程广义行波的稳定性和唯一性

发布时间：2018-03-16 08:04

  本文选题：非均匀介质　切入点：离散Fisher-KPP方程　出处：《中国科学:数学》2017年12期 　论文类型：期刊论文

【摘要】：本文研究具有一般时间和空间依赖性离散Fisher-KPP(Kolmogorov-Petrovsky-Piskunov简写为KPP)方程广义行波的稳定性和唯一性.首先证明此类方程严格正整体解的存在性、唯一性和稳定性;接着建立连接此唯一严格正整体解和平凡零解的广义行波的稳定性和唯一性.应用广义行波的一般性稳定性和唯一性理论,本文进而证明时间和空间周期介质中离散Fisher-KPP方程周期行波解的存在性、稳定性和唯一性,以及时间非均匀介质中离散Fisher-KPP方程广义行波的存在性、稳定性和唯一性.本文所建立的一般性稳定性和唯一性理论表明在很多情形下得到的广义行波在合适的扰动下是渐近稳定的.
[Abstract]:In this paper, we study the stability and uniqueness of generalized traveling waves for discrete Fisher-KPP(Kolmogorov-Petrovsky-Piskunov equations with general temporal and spatial dependence. Firstly, we prove the existence, uniqueness and stability of strictly positive global solutions for such equations. Then the stability and uniqueness of the generalized traveling wave connecting the unique positive global solution and the trivial zero solution are established. The general stability and uniqueness theory of the generalized traveling wave is applied. In this paper, we prove the existence, stability and uniqueness of periodic traveling wave solutions of discrete Fisher-KPP equation in time and space periodic media, and the existence of generalized traveling waves of discrete Fisher-KPP equation in time-inhomogeneous media. The theory of general stability and uniqueness established in this paper shows that the generalized traveling waves obtained in many cases are asymptotically stable under suitable perturbation.
【作者单位】： 南京航空航天大学数学系;Department
【基金】：国家自然科学基金(批准号:11201226)资助项目
【分类号】：O175
，

本文编号：1619030