Linearized Stability of Extreme Shock Profiles for Systems of Conservation Laws with Viscosity.

Abstract

For a genuinely nonlinear hyperbolic system of conservation laws with added artificial viscosity, we prove that traveling wave profiles for small amplitude extreme shocks (the slowest and fastest) are linearly stable to perturbations initial data chosen from certain spaces with weighted norm; i.e., we show that the spectrum of the linearized equation lies strictly in the left half plane, except for a simple eigenvalue at the origin (due to phase translations of the profile). The weight is used in components transverse to the profile, where, for an extreme shock, the linearized equation is dominated by unidirectional convection.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1982
Accession Number
ADA125256

Entities

People

  • Robert L. Pego

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Analytic Functions
  • Banach Space
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Inequalities
  • Integral Equations
  • Materials
  • Mathematics
  • Perturbation Theory
  • Perturbations
  • Scalar Functions
  • Standards
  • Traveling Waves
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space