Systems of Three First-Order Partial Differential Equations with Three Unknown Functions and Two Independent Variables (Local Theory).

Abstract

The systems indicated in the title (denoted by S sub (3, 2)) are studied by the Cartan method. The problems solved in the article are characteristic for the geometric theory of differential equations; many constructions can be carried over to other classes of systems of differential equations. This is especially true of the beginning of section 1, which contains constructions applicable to a broad class of differential-geometric studies. These constructions are a specialization of the general scheme of study of families of geometric objects. Studied in part 2 are quasilinear systems having non-coinciding characteristics. The end of the section contains a necessary and sufficient condition for systems that reduce to linear systems. Considered in section 3 are questions connected with laws of conservation for quasilinear systems. The concept of a generalized stream function is introduced and the part it plays is outlined. Several systems encountered in mechanics are examined in section 4. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 19, 1971
Accession Number
AD0735508

Entities

People

  • A. M. Vasilev

Organizations

  • Johns Hopkins University Applied Physics Laboratory

Tags

DTIC Thesaurus Topics

  • Construction
  • Differential Equations
  • Equations
  • Linear Systems
  • Mathematics
  • Mechanics
  • Partial Differential Equations

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Plasma Physics / Magnetohydrodynamics
  • Theoretical Analysis.