On the Existence and Compactness of a Two-Dimensional Resonant System of Conservation Laws

Abstract

We prove the existence of a weak solution to a two-dimensional resonant 3 3 system of conservation laws with BV initial data. Due to possible resonance (coinciding eigenvalues), spatial BV estimates are in general not available. Instead, we use an entropy dissipation bound combined with the time translation invariance property of the system to prove existence based on a two-dimensional compensated compactness argument adapted from E. Tadmor, M. Rascle, and P. Bagnerini, 2005. Existence is proved under the assumption that the flux functions in the two directions are linearly independent.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 2006
Accession Number
ADA457740

Entities

People

  • Eitan Tadmor
  • Kenneth H. Karlsen
  • Michel Rascle

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Abstracts
  • Blood Flow
  • Coefficients
  • Convergence
  • Eigenvalues
  • Equations
  • Flow
  • Gas Flow
  • Inequalities
  • Information Operations
  • Intervals
  • Mathematics
  • Sequences
  • Standards
  • Translations
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Microwave Engineering.