Dissertation > Excellent graduate degree dissertation topics show

The long time behavior of the finite difference scheme for three - dimensional reaction-diffusion equation with nonlinear terms in the polynomial

Author: WangZuo
Tutor: ZhangFaYong
School: Heilongjiang University
Course: Basic mathematics
Keywords: Global attractor Reaction-diffusion equation Finite diference scheme Stability and convergence
CLC: O241.8
Type: Master's thesis
Year: 2006
Downloads: 60
Quote: 0
Read: Download Dissertation

Abstract


In this paper, a three-dimensional reaction-diffusion equation with a polynomial nonlinearity that possesses a global attractor is considered.The existence of an attractor is one of the most important characteristics for a dissipative system,the long-time dynamics is completely determined by the attractor of the system.At present,most studies are linked to the semi-discrete scheme and the one-dimensional spatial variable.But,there are very few studies about the full-discrete scheme and the higher dimensional spatial variable. Furthermore,the former can’t be extended directly to the latter.As the result,the latter is focused by the reseachers nowadays.The dynamical properties of the discrete dynamical system which is generated by a finite difference scheme are analysed.First,we construct the finite difference scheme of the equation,the existence and the uniqueness of the solution for the scheme are proved.Then,the existence of an absorbing set in the space of L_h~2-functions and H_h~1-functions is drawn.Therefore,the existence of an attractor of the equation in three-dimensional space is obtained by using the conclusion in[1].Finally,long-time stability and convergence of the finite difference scheme is proved.

Related Dissertations

  1. Global Attractor of the Cauchy Problem for a Class of Nonlinear Fourth Order Wave Equation,O175.29
  2. Higher-Order Monotone Iterative Methods for Numerical Solutions of Nonlinear Reaction-Diffusion Equations with Time Delay,O241.82
  3. The Global Attractor of Strongly Damped Nonlinear Thermoelastic Coupled Rod System,O175.2
  4. Asymptotic properties of a class of reaction-diffusion equation spectral method of solutions and error estimates prolonged,O241.8
  5. Global Behavior of Some Nonlinear Delay Difference Equation,O175.7
  6. Random Attractors of Cahn-Hilliard Equations,O175.29
  7. Existence, Uniqueness and Long Time Behaviour of the Positive Weak Solutions of a Nonlinear Reaction-diffusion Equation with Singular Term,O175.26
  8. Long-time Behavior of Solution for Reaction-diffusion Equation with Nonlinear Boundary Conditions,O175.29
  9. Existence of Global Attractor for Partly Dissipative Reaction Diffusion System in Unbounded Domain,O175.29
  10. On the Existence of Pullback Attractors for Nonautonomous Infinite Dimensional Dynamical Systems,O177.91
  11. Application of Homotopy Analysis Method for Some Nonlinear Problems in Fluid Mechanics,O35
  12. Qualitative Analysis of Steady-State Patterns of Some Prey-Predator Models,O175
  13. The Global Attractors for Some Nonlinear Evolution Equations,O175
  14. The Unbounded Domain rational spectral method,O241.82
  15. Study on Problems of Global Attractors for Wave Equations with Nonlinear Damping,O19
  16. Dynamical Behavior for Three Dimensional Ginzburg-Landau Equation,O19
  17. The Global Solutions and Their Properties for Camassa-Holm Equations and Ginzburg-Landau Equations,O175.8
  18. Existence of Periodic Solutions and Regularity of Global Attractors for the Derivative Ginzburg-Landau Equations,O175.29
  19. Research on Routing Optimization in Large Scale Autonomous Systems,TP393.02
  20. Lattice Boltzmann Method for Reaction-Diffusion Equation and Its Numerical Simulations,O552.2

CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations
© 2012 www.DissertationTopic.Net  Mobile