FRACTAL DIMENSIONS OF THE REACTION-DIFFUSION EQUATIONS

• Otsubo Toshimasa

  Department of Mathematics Keio University

• Tani Atusi

  Department of Mathematics Keio University

• Nodera Takashi

  Department of Mathematics Keio University

Bibliographic Information

Other Title

• Reaction-Diffusion EquationsのFractal次元

Abstract

In this paper, we study the Fractal (Hausdorff) Dimension of the Reaction-Diffusion Equations ((∂u)/(∂t)-νΔu+g(u,x)=0). In particular, we discuss the Lorenz type equations. First, we will show the existence of the solutions and the attractors of the Lorenz type equations. We linearize these equations and it is concerned with Lyapunov Exponent. Then, it gives us the Fractal (Hausdorff) Dimension. Finally, we will give you some numerical experiments of this dimension (It depends on the viscosity ν or the constants of nonlinear term σ, b, r). We can show that when ν=0 these equations coincides with the Lorenz Model (Hausdorff dimension of Lorenz Model is 2.538, where σ=10, b=8/3, r=28).

Journal

• IPSJ SIG Notes

  IPSJ SIG Notes 94 (108), 1-6, 1994-12-14

  Information Processing Society of Japan (IPSJ)

Details

• CRID: 1571417127177332864
• NII Article ID: 110002932155
• NII Book ID: AN10463942
• Text Lang: ja
• Data Source:
  • CiNii Articles