Homogeneous and Non-Homogeneous Boundary Value Problems for First Order Linear Hyperbolic Systems Arising in Fluid Mechanics. Part II.

Abstract

We prove the existence and the uniqueness of differentiable and strong solutions for a class of boundary value problems for first order linear hyperbolic systems arising from the dynamics of compressible non-viscous fluids. In particular necessary and sufficient conditions for the existence of solutions for the non-homogeneous problem are studied; strong solutions are obtained without this supplementary condition. In particular we don't assume the boundary space to be maximal non-positive and the boundary matrix to be of constant rank on the boundary. In this paper we prove directly the existence of differentiable solutions without resort to weak or strong solutions. An essential tool will be the introduction of a space Z of regular functions verifying not only the assigned boundary conditions but also some suitable complementary boundary conditions.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1982
Accession Number
ADA116322

Entities

People

  • H. Beirao Da Veiga

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Banach Space
  • Boundary Value Problems
  • Cauchy Problem
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Equations
  • Fluid Mechanics
  • Formulas (Mathematics)
  • Functional Analysis
  • Hilbert Space
  • Integral Equations
  • Mathematics
  • Mechanics
  • Partial Differential Equations
  • United States
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space