Nonlinear Partial Differential Equations for Gas and Elasticity

Abstract

We obtain a striking new phenomenon that a perturbation of such a wave produces another wave with same given end states without other time- asymptoti state. This is markedly distinct from the vicous shock waves in gas flow. The author subsequently studied the overcompressive shocks in a MHD and elasticity model. Such a wave is called intermediate shock wave, whose admissibility has been controversial since the 1950's. One of the main research interests of the author in recent years has been the qualitative understanding of viscous conservation laws such as the compressible Navier-Stokes equations. Usual approach uses typical parabolic techniques such as spectral and energy methods, or maximum principle. These methods are of limited effectiveness because they fail to detect the hyperbolic mature of underlying inviscid models. A new approach is introduced to incorporate the nonlinear coupling of waves pertaining to different characteristics families, such as nonlinear acoustic wave and entropy waves in gas flow.

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Document Details

Document Type
Technical Report
Publication Date
Dec 31, 1990
Accession Number
ADA241791

Entities

People

  • Tai-ping Liu

Organizations

  • New York University

Tags

DTIC Thesaurus Topics

  • Acoustic Waves
  • Cauchy Problem
  • Couplings
  • Differential Equations
  • Elastic Properties
  • Equations
  • Flow
  • Gas Flow
  • Navier Stokes Equations
  • New York
  • Partial Differential Equations
  • Shock
  • Shock Waves
  • Waves

Fields of Study

  • Mathematics

Readers

  • Combustion Dynamics and Shock Wave Physics.
  • Fluid Dynamics.
  • Systems Analysis and Design