Regularity for a Singular Conservation Law,

Abstract

The main structure underlying the nonlinearity of conservation laws of gasdynamical type in two independent variables is discussed at the hand of a canonical example describing also properties of water waves near shore. The ultimately singular nature of such laws is here the central issue and calls for an unusual formulation. Attention is directed to the globally strong solutions, and an unusual regularization is employed to make them accessible, after illposedness is overcome. The usual regularity theory is not normally sufficient for singular partial differential equations, and the neccessry additional chapter on extensions to the singular locus is developed in detail for the canonical example. Criteria for the relation between regularized and strong solutions are discussed and used to characterize the class of solutions that are globally strong in the strictest sense. Keywords: Nonlinear partial differential equations; Waves on beaches.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1985
Accession Number
ADA163620

Entities

People

  • R. E. Meyer

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Coefficients
  • Differential Equations
  • Engineering
  • Equations
  • Flow Rate
  • Formulas (Mathematics)
  • Gas Dynamics
  • Mass Flow
  • Mathematics
  • New York
  • Partial Differential Equations
  • Supersonic Flow
  • Two Dimensional
  • United States
  • Water Waves
  • Wave Equations
  • Waves

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Coastal and Marine Engineering/Sediment Transport/Hydraulic Engineering