本文選題：非均勻介質(zhì)　切入點(diǎn)：離散Fisher-KPP方程　出處：《中國科學(xué):數(shù)學(xué)》2017年12期 　論文類型：期刊論文

【摘要】：本文研究具有一般時(shí)間和空間依賴性離散Fisher-KPP(Kolmogorov-Petrovsky-Piskunov簡寫為KPP)方程廣義行波的穩(wěn)定性和唯一性.首先證明此類方程嚴(yán)格正整體解的存在性、唯一性和穩(wěn)定性;接著建立連接此唯一嚴(yán)格正整體解和平凡零解的廣義行波的穩(wěn)定性和唯一性.應(yīng)用廣義行波的一般性穩(wěn)定性和唯一性理論,本文進(jìn)而證明時(shí)間和空間周期介質(zhì)中離散Fisher-KPP方程周期行波解的存在性、穩(wěn)定性和唯一性,以及時(shí)間非均勻介質(zhì)中離散Fisher-KPP方程廣義行波的存在性、穩(wěn)定性和唯一性.本文所建立的一般性穩(wěn)定性和唯一性理論表明在很多情形下得到的廣義行波在合適的擾動(dòng)下是漸近穩(wěn)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.
【作者單位】： 南京航空航天大學(xué)數(shù)學(xué)系;Department
【基金】：國家自然科學(xué)基金(批準(zhǔn)號(hào):11201226)資助項(xiàng)目
【分類號(hào)】：O175
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本文編號(hào)：1619030