Nonlinear Waves in Mechanics and Gas Dynamics

Abstract

The proposer has studied nonlinear hyperbolic-parabolic partial differential equations related to gas dynamics and mechanics. Hyperbolic conservation laws with relaxation are studied with applications to kinetic theory, elasticity with memory and gas flow with thermo-non-equilibrium in mind. Nonlinear waves for the compressible Navier-Stokes equations are studied for their stability and time-asymptotic behavior. The singular behavior of the magenetohydrodynamics shock waves in the small dissipation limits is clarified, in particular, it is shown that intermediate shocks are stable uniformly with regards to the strength of dissipations only for 2-dimensional model, and not for 3-dimensional model.

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Document Details

Document Type
Technical Report
Publication Date
Dec 21, 1990
Accession Number
ADA238340

Entities

People

  • Tai-ping Liu

Organizations

  • University of Maryland

Tags

DTIC Thesaurus Topics

  • Cauchy Problem
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Elastic Properties
  • Electrical Solitons
  • Equations
  • Flow
  • Fluid Dynamics
  • Fluid Mechanics
  • Gas Flow
  • Kinetic Theory
  • Mechanics
  • Navier Stokes Equations
  • Partial Differential Equations
  • Shock Waves
  • Waves

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Dynamics.