Homogenization for Semilinear Hyperbolic Systems with Oscillatory Data

Abstract

The behavior of multi-dimensional discrete Boltzmann systems with highly oscillatory data is studied. Homogenized equations for the mean solutions are obtained. Uniform convergence of the oscillatory solutions of the discrete Boltzmann equations to the solutions of the corresponding homogenized equations is established. Moreover, we find that the weak limits of the oscillatory solutions for a model of Broadwell type are not continuous functions of the discrete velocities. Generalization of the above results to problems with multiple-scale initial data is also established. Reprints.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1988
Accession Number
ADA201299

Entities

People

  • Thomas Y. Hou

Organizations

  • New York University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Applied Mathematics
  • Boltzmann Equation
  • Coefficients
  • Collisions
  • Convergence
  • Differential Equations
  • Equations
  • Frequency
  • Gases
  • Irrational Numbers
  • Mathematics
  • Numbers
  • Partial Differential Equations
  • Periodic Functions
  • Rational Numbers
  • Real Numbers
  • Theorems

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)