Center for Nonlinear Phenomena and Magnetic Materials

Abstract

In previous work we have proved existence and obtained estimates for the (finite) Huasdorff and fractal dimensions of global (maximal compact) attractors for the Landau-Lifschitz equations. These are the fundamental equations of the classical theory ferromagnetism. In order to obtain more detailed information about these attractors, we are currently developing approximation methods based on the theory of inertial manifolds. Inertial manifolds are finite dimensional manifolds which attract all solutions at an exponential rate. They contain the global attractor and have the advantage that they are manifolds whereas the attractors generally are not(they can be complicated fractal sets). The equations reduce to a finite-dimensional system of O.D.E.'s on the inertial manifolds.

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Document Details

Document Type
Technical Report
Publication Date
Dec 04, 1992
Accession Number
ADA274176

Entities

People

  • Tepper L. Gill

Organizations

  • Howard University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Banach Space
  • Computational Science
  • Differential Equations
  • Electrical Engineering
  • Elementary Particles
  • Engineering
  • Equations
  • High Performance Computing
  • Magnetic Materials
  • Magnetic Phenomena
  • Materials
  • Mathematics
  • Navier Stokes Equations
  • Partial Differential Equations
  • Path Integrals
  • Signal Processing
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)