Boundary Value Problems and Free Boundary Problems for Quasilinear Hyperbolic-Parabolic Coupled Systems.

Abstract

In many applications one meets systems of differential equations which consist of first-order hyperbolic and second-order parabolic subsystems which are nonlinearly coupled. These arise, for instance, in the modeling of motion of a compressible, viscous heat conducting fluid, in radiation hydrodynamics, and in the theory of motion of viscoelastic materials. The relevant equations are presented. The results of this work are local time existence and uniqueness theorems for initial-boundary value problems, including cases with free boundaries, for such systems. The results given are for the case of one space dimension. The methods used involve introducing appropriate variables, the method of iteration, a priori estimation and fixed point theorems.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1981
Accession Number
ADA110482

Entities

People

  • Ta-tsien Li
  • We-shi Shen
  • Wen-tzu Yu

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Autonomy
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Coefficients
  • Directional
  • Equations
  • Formulas (Mathematics)
  • Geometry
  • High Temperature
  • Hydrodynamics
  • Materials
  • Mathematics
  • Point Theorem
  • Radiation
  • Theorems
  • United States
  • Wisconsin

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space