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.
In this paper, we investigate the stability and uniqueness of generalized traveling wave solutions of lattice Fisher-KPP equations with general time and space dependence. We first show the existence, uniqueness,and stability of strictly positive entire solutions of such equations. Next, we show the stability and uniqueness of generalized traveling waves connecting the unique strictly positive entire solution and the trivial solution zero.Applying the general stability and uniqueness theorem, we then prove the existence, stability and uniqueness of periodic traveling wave solutions of lattice Fisher-KPP equations in time and space periodic media, and the existence, stability and uniqueness of generalized traveling wave solutions of lattice Fisher-KPP equations in time heterogeneous media. The general stability and uniqueness results established in this paper imply that the generalized traveling waves obtained in many cases are asymptotically stable under well-fitted perturbation.
出处
《中国科学：数学》
CSCD
北大核心
2017年第12期1787-1808,共22页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11201226)资助项目
