Dissertation > Excellent graduate degree dissertation topics show
The Stability of Travelling Waves for Generalized Fisher Equation(Systems) and Viscous Balance Law
Author: XingXiuXia
Tutor: WuYaPing
School: Capital Normal University
Course: Basic mathematics
Keywords: Traveling wave solutions Algebraic decay Spectral analysis Evans function Semigroup Comparison principle Asymptotically stable Global stability
CLC: O175.1
Type: PhD thesis
Year: 2005
Downloads: 117
Quote: 6
Read: Download Dissertation
Abstract
This article consists of three parts: the first part of the study before the generalized Fisher equation wave asymptotic stability of. The classic spectral analysis method and semigroup methods combined, we have been traveling wave solutions with critical and noncritical wave speed in the weighted space the locally asymptotically index stability. On this basis, the use of the comparison principle, prove the critical wave speed traveling wave solutions exponentially weighted space of global asymptotic stability. Further, the Evans function method, the appropriate space decomposition semigroup method and the classic combination of spectral analysis method, we were obtained the locally asymptotically algebra with critical and noncritical wave speed traveling wave solutions in polynomial weighted space stability. Stability of traveling wave solutions with noncritical wave speed in the study, due to the traveling wave attenuation ∞ algebra at a slower rate, which leads to research linearization operator eigenvalue problem, often not directly based on the classic asymptotic theory of differential equations to determine the solution of the eigenvalue problem ∞ the asymptotic behavior, making it impossible to define the Evans function. By using more general asymptotic theory of ordinary differential equations, we get a detailed portrait ∞ the asymptotic behavior of the solution of the eigenvalue problem. Based on this, we can define the Evans function to construct the Evans function here and prove that the same has to resolve, and still corresponding linear operator eigenvalues ??zero, which indicates that the Evans function definition is extended to more general situation. Stability of traveling wave solutions in the critical wave speed, we verify that the Evans function D (λ) has some important properties of linear operator of the MS is not zero, especially at the origin: D (0 ) = 0, but D_λ (0) ≠ 0, this to the appropriate spatial decomposition and semigroup estimate is very useful. The second part of a class of viscous balance law equation asymptotic stability of traveling wave solutions. First, the nature of the use of the method of spectral analysis, comparison principle, and ωlimit sets, we prove asymptotic exponential stability of traveling wave solutions for the global general viscous balance law equation connecting the saddle point, this results generalize the classic reactiondiffusion saddle saddle wave equation global stability results. Secondly, we study the existence and stability of viscous balance law of traveling wave solutions degraded. Phase plane analysis, we obtain the existence of solutions in its wavefront. On this basis, the use of the Evans function method, semigroup method and the method of spectral analysis, similar to the first part, we obtain the local asymptotic stability of traveling wave solutions exponentially weighted space and polynomial weighted space. Stability of traveling wave solutions of the third part of the study of a class of selfcatalytic chemical reaction equations. Clever spectral analysis and semigroup theory, we get the diffusion coefficient d = 1 has local asymptotic critical wave speed and noncritical Traveling Waves in the appropriate weighted space exponential stability; addition, we preliminarily diffusion The coefficient d ≠ the spectral properties of the linearity of the operator.

Related Dissertations
 Convergence and Stability of Numerical Solution of Stochastic Differential Equations with Piecewise Continuous Arguments,O211.63
 The Study on Rhinoceros Horn and Its Imitation,TS932.2
 M1 of CRH2300 Train Finite Element Analysis and Travelling Comfort,U266
 Formalization of the SoS Framework Approach,TP393.09
 Data Driven Rolling Bearing Fault Diagnosis Research,TH165.3
 Periodic fluctuations in interest rates compared with the United States,F837.12;F224
 SWATH catamaran Fatigue Analysis and Optimization of a typical node,U674.951
 Research on DBS Imaging Technique for MMW Terminal Guidance Radar,TJ761.14
 Optimal Control for Stable Solution of Repairable HumanMachine Systems,O232
 On the Study of Asymptotically Stable for Fractionalorder Neutral Retarded Dynamic Systems,O19
 Finite TypeA Semigroup Algebras,O152.7
 Qualitative Analysis on the Predatorprey Systems with Undercrowding Effect,O175.1
 Local Existence of Solutions to the Magnetohydrodynamic Equation in R_{+}^{n+1},O175.2
 A class of singular semilinear reactiondiffusion equations Cauchy problem,O175.2
 Behavior Analysis and Optimal Control of Biological Population Dynamical Systems with SizeStructure,O232
 Research on the Bifurcations of Traveling Wave Solutions for Several Classes of Nonlinear Wave Equations,O175.29
 Global Stability of Differential Equations with Piecewise Continuous Arguments and the Convergence of Exponential RungeKutta,O241.8
 The Transmission Dynamics of H1N1,O175
 The Study of Asymptotical Behaviors on Several Classes of Nonautonomous Difference Competitive System,O175.7
 Stability of Dynamic Systems on Time Scales,O19
 The Construction of Right Processes,O211.62
CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Ordinary Differential Equations
© 2012 www.DissertationTopic.Net Mobile
