【摘要】：本文考慮了兩類非線性拋物方程解的漸進性質及平衡態(tài).首先我們考慮了一類多孔介質方程解的全局存在與爆破條件.對于該方程在初始能量E(u0)d時的全局存在與爆破條件已有很多研究,其中E(u0)表示初始能量,d是將在正文中給出的一個正常數(shù).本文主要針對初始能量E(u0)=d進行研究并給出了解的全局存在與爆破條件.其次我們研究了具有分數(shù)型交錯擴散的Lotka-Volterra捕食-食餌模型解的情況.通過分析該模型的線性化問題的特征值問題,并利用分支理論和拓撲度理論我們研究了該模型的正平衡態(tài)解的性質,并得到了正平衡態(tài)解的多重性條件,此結論推廣并完善了已有結果.再次我們研究了交錯擴散系數(shù)對共存區(qū)域的影響,并給出了極限系統(tǒng)的局部分支理論.全文共分為三個部分:·第一章,主要介紹多孔介質方程和具有分數(shù)型交錯擴散Lotka-Volterra捕食-食餌模型的背景,創(chuàng)新之處.·第二章,主要討論多孔介質方程的解的全局存在與爆破條件.·第三章,主要討論具有分數(shù)型交錯擴散Lotka-Volterra的捕食-食餌模型解的多重性與交錯擴散系數(shù)對共存區(qū)域的影響.
[Abstract]:In this paper, the asymptotic property and equilibrium state of solutions for two classes of nonlinear parabolic equations are considered. First, we consider the global existence and blasting conditions of solutions for a class of porous media equations. Many studies have been done on the global existence and blasting conditions of the equation at the initial energy E (u 0) d, where E (u 0) denotes the initial energy and d is a normal number to be given in the text. In this paper, the initial energy E (u 0) = d is studied and the global existence and blasting conditions of the solution are given. Secondly, we study the solution of Lotka-Volterra predator-prey model with fractional staggered diffusion. By analyzing the eigenvalue problem of the linearization problem of the model, and using the bifurcation theory and topological degree theory, we study the properties of the positive equilibrium solution of the model, and obtain the conditions of multiplicity of the positive equilibrium solution. This conclusion extends and improves the existing results. Thirdly, we study the influence of staggered diffusion coefficient on coexisting region, and give the local bifurcation theory of limit system. The thesis is divided into three parts: chapter 1, mainly introduces the porous medium equation and the background and innovation of the Lotka-Volterra predator-prey model with fractional staggered diffusion. The global existence and blasting conditions of solutions for porous media equations are discussed. In chapter 3, the multiplicity of solutions of predator-prey models with fractional staggered diffusion Lotka-Volterra and the influence of staggered diffusion coefficients on coexisting regions are discussed.
【學位授予單位】：西南大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O175.26

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本文編號：2330790