Systems of Three First-Order Partial Differential Equations with Three Unknown Functions and Two Independent Variables (Local Theory).
R. E. Gibson Library bulletin translation series,
JOHNS HOPKINS UNIV SILVER SPRING MD APPLIED PHYSICS LAB
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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
- Theoretical Mathematics