Accession Number : AD0735508

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

Descriptive Note : R. E. Gibson Library bulletin translation series,

Corporate Author : JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB

Personal Author(s) : Vasilev,A. M.

Report Date : 19 APR 1971

Pagination or Media Count : 37

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)

Descriptors :   (*PARTIAL DIFFERENTIAL EQUATIONS, DIFFERENTIAL GEOMETRY), INTEGRALS, OPERATORS(MATHEMATICS), VECTOR SPACES, TRANSFORMATIONS(MATHEMATICS), USSR

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE