On the global solubility of the Monge-Ampere hyperbolic equations
| Autor: | D V Tunitskii |
|---|---|
| Rok vydání: | 1997 |
| Předmět: |
Cauchy problem
Independent equation General Mathematics Weak solution Mathematical analysis Mathematics::Analysis of PDEs Euler equations Examples of differential equations symbols.namesake Elliptic partial differential equation Linear differential equation symbols Applied mathematics Hyperbolic partial differential equation Mathematics |
| Zdroj: | Izvestiya: Mathematics. 61:1069-1111 |
| ISSN: | 1468-4810 1064-5632 |
| DOI: | 10.1070/im1997v061n05abeh000163 |
| Popis: | This paper is devoted to the solubility of the Cauchy problem for the Monge-Ampere hyperbolic equations, in particular, for quasi-linear equations with two independent variables. It is proved that this problem has a unique maximal solution in the class of multi-valued solutions. The notion of a multi-valued solution goes back to Monge, Lie, et al. It is an historical predecessor of the notion of a generalized solution in the Sobolev-Schwartz sense. The relationship between multi-valued and generalized solutions of linear differential equations is established. |
| Databáze: | OpenAIRE |
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