Hyperbolic Conservation Laws with Umbilic Points I

Abstract

In this paper a compactness framework for approximate solutions to nonlinear hyperbolic systems with umbilic points is established by combining ideas in modern nonlinear analysis with classical methods, and by a detailed analysis of a highly singular Euler-Poisson-Darboux-type equation. Then this framework is successfully applied to prove the convergence of the Lax-Friedrichs scheme, the Godunov scheme and the viscosity method, and the existence of global entropy solutions for the Cauchy problem with large initial data for a canonical class of the quadratic flux systems and other related systems. In forthcoming papers CK1, CK2, we apply (a variant of) this framework to solve the other three canonical classes of the quadratic flux systems, the system of three-phase flow in porous media and other related systems with umbilic points.

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1992
Accession Number
ADA254431

Entities

People

  • Gui-Qiang Chen
  • Pui T. Kan

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Analytic Functions
  • Boundary Value Problems
  • Cauchy Problem
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Eigenvalues
  • Equations
  • Flow
  • Fluid Dynamics
  • Formulas (Mathematics)
  • Gas Dynamics
  • Geometry
  • Mathematics
  • Power Series
  • Sequences
  • Shock Waves

Fields of Study

  • Mathematics

Readers

  • Aerospace Engineering
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)