本文關(guān)鍵詞：非齊次環(huán)境下兩種群競爭系統(tǒng)的行波解　出處：《蘭州大學》2016年博士論文　論文類型：學位論文

  更多相關(guān)文章： 兩種群競爭系統(tǒng) 行波解 時間周期 空間周期 存在性 穩(wěn)定性

【摘要】：反應擴散系統(tǒng)廣泛應用于許多自然科學,包括生物,化學和物理等.行波解是反應擴散方程系統(tǒng)的一種特殊形式的解并且已被廣泛用來模擬許多自然現(xiàn)象.特別地,在燃燒理論,化學反應等的實驗觀察和數(shù)值計算中已經(jīng)發(fā)現(xiàn)了許多具有不同形狀水平集的行波解.此外,現(xiàn)實的自然環(huán)境是隨著時間和空間變化而變化的.因此研究非齊次環(huán)境下反應擴散方程系統(tǒng)的非平面波具有重要的現(xiàn)實意義.兩種群競爭系統(tǒng)是用來模擬兩個或多種群相互作用的一類重要模型.本文首先將研究時間周期環(huán)境下兩種群競爭系統(tǒng)的時間周期非平面行波解.另一方面,非局部擴散發(fā)展系統(tǒng)也廣泛用于模擬種群在非鄰近區(qū)域的相互作用.本文也將研究具有非局部擴散的兩種群競爭系統(tǒng)在空間周期環(huán)境下的空間周期行波解.本文首先研究了時間周期的兩種群擴散系統(tǒng)在二維空間中的時間周期V形行波解.為此,本文建立了系統(tǒng)一維時間周期行波解在無窮遠處的漸近行為.然后通過構(gòu)造適當?shù)纳舷陆?證明時間周期的二維曲面行波解的存在性.進一步,我們證明了時間周期曲面行波解是漸近穩(wěn)定并唯一的.其次研究了時間周期兩種群擴散系統(tǒng)在高維空間RN(N≥3)中的時間周期棱錐形行波解.利用比較原理并構(gòu)造適當?shù)纳舷陆?證明了在RN中時間周期兩種群擴散系統(tǒng)存在時間周期棱錐形行波解并給出了時間周期棱錐形行波解所滿足的定性性質(zhì).最后研究了具有非局部擴散的兩種群爭系統(tǒng)在空間周期環(huán)境下的空間周期行波解.在適當?shù)募僭O(shè)下,系統(tǒng)存在兩個空間周期的半平凡平衡解(u*1(x),0)和(0,u*2(x)),其中(u*1(x),0)是線性并全局漸近穩(wěn)定的而(0,u*2(x))在空間周期擾動下是線性不穩(wěn)定的.利用上下解技術(shù)和比較原理,對每個ξ∈SN-1,證明系統(tǒng)存在連接(u*1(x),0)和(0,u*2(x))并在ξ方向以波速cc*(ξ)傳播的空間周期行波解,其中c*(ξ)是系統(tǒng)在ξ方向的傳播速度.另外,對cc*(ξ),系統(tǒng)不存在這樣的行波解.當波速cc*(ξ),利用擠壓方法也證明了空間周期行波解的漸近穩(wěn)定性和唯一性.
[Abstract]:Reaction-diffusion systems are widely used in many natural sciences, including biology. The traveling wave solution is a special form of solution of the reaction-diffusion equation system and has been widely used to simulate many natural phenomena, especially in the combustion theory. Many traveling wave solutions with different shape horizontal sets have been found in the experimental observation and numerical calculation of chemical reactions. The natural environment of reality changes with time and space. Therefore, it is of great practical significance to study the nonplane wave of the reaction-diffusion equation system in a non-homogeneous environment. The two-species competition system is used to simulate two or two species. In this paper, we first study the time-periodic nonplanar traveling wave solutions of a two-species competitive system in a time-periodic environment. Non-local diffusion development systems are also widely used to simulate the interaction of populations in non-adjacent regions. In this paper, we will also study the spatial periodic traveling wave solutions of two species competitive systems with non-local diffusion in spatial periodic environment. In this paper, the time-periodic V-shaped traveling wave solutions of a time-periodic two-species diffusion system in two-dimensional space are studied. In this paper, the asymptotic behavior of one-dimensional time-periodic traveling wave solutions at infinity is established, and then the existence of time-periodic two-dimensional surface traveling wave solutions is proved by constructing appropriate upper and lower solutions. We prove that the traveling wave solution of time-periodic surface is asymptotically stable and unique. Secondly, we study the time-periodic two-species diffusion system with RN(N 鈮，

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