Decay with a Rate for Noncompactly Supported Solutions of Conservation Laws.

Abstract

This document shows that solutions of the Cauchy problem for systems of two conservation laws decay in the supnorm at a rate that depends only on the L sub 1 norm of the initial data. This implies that the dissipation due to the entropy dominates the nonlinearities in the problem at a rate depending only on the L sub 1 norm of the initial data. The main estimate requires an analysis of approximate characteristics for its proof. A general framework is developed for the study of approximate characteristics, and the main estimate is obtained for an arbitrary number of equations. Keywords: Riemann Problem; Random Choice Method; Decay; Stability; Continuous Dependence; Conservation Laws; nonlinear partial differential equations.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1985
Accession Number
ADA158163

Entities

People

  • B. Temple

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boundary Value Problems
  • Cauchy Problem
  • Classification
  • Coordinate Systems
  • Differential Equations
  • Dissipation
  • Equations
  • Formulas (Mathematics)
  • Gas Dynamics
  • Lepidoptera
  • Materials
  • Mathematics
  • Partial Differential Equations
  • Shock
  • Shock Waves
  • United States
  • Waves

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)