On the integrability problem for systems of partial differential equations in one unknown function, I
| Autor: | Antonio Kumpera |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Work (thermodynamics)
Partial differential equation Pfaffian system lcsh:Mathematics Applied Mathematics 010102 general mathematics Cauchy distribution Function (mathematics) local equivalence Integration problem lcsh:QA1-939 First order Partial differential equations 01 natural sciences 010305 fluids & plasmas contact structures Grassmannian 0103 physical sciences Systems of partial differential equations Applied mathematics Geometry and Topology 0101 mathematics Analysis Mathematics |
| Zdroj: | Pracì Mìžnarodnogo Geometričnogo Centru, Vol 11, Iss 4, Pp 35-71 (2018) |
| ISSN: | 2409-8906 2072-9812 |
| DOI: | 10.15673/tmgc.v11i4.1305 |
| Popis: | We discuss the integration problem for systems of partial differential equations in one unknown function and special attention is given to the first order systems. The Grassmannian contact structures are the basic setting for our discussion and the major part of our considerations inquires on the nature of the Cauchy characteristics in view of obtaining the necessary criteria that assure the existence of solutions. In all the practical applications of partial differential equations, what is mostly needed and what in fact is hardest to obtains are the solutions of the system or, occasionally, some specific solutions. This work is based on four most enlightening Mémoires written by Élie Cartan in the beginning of the last century. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|