| ISSN 1683-3414 (Print) • ISSN 1814-0807 (Online) | |||
![]() |
![]() |
![]() |
|
| Log in | |||
ContactsAddress: Vatutina st. 53, Vladikavkaz,
|
DOI: 10.46698/t8227-2101-5573-p Solvability of Cauchy Problem for One System of First Order Quasilinear Differential Equations
Dontsova, M. V.
Vladikavkaz Mathematical Journal 2021. Vol. 23. Issue 3.
Abstract:
We consider the Cauchy problem for a system of first-order quasilinear differential equations. The solvability of the problem is investigated in the initial coordinates using the additional argument method. Sufficient conditions for the existence and uniqueness of a local solution which has the same smoothness in the independent variable as the initial functions of the Cauchy problem are determined. An existence and uniqueness theorem of a local solution is proved. Sufficient conditions for the existence and uniqueness of a global solution are determined. The proof of the global solvability relies upon global estimates.
Keywords: method of an additional argument, Cauchy problem, first-order partial differential equation
Language: Russian
For citation: Dontsova, M. V. Solvability of Cauchy Problem for One System of First Order Quasilinear Differential Equations, Vladikavkaz Math. J., 2021, vol. 23, no. 3, pp. 64-79.
DOI 10.46698/t8227-2101-5573-p
The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue |
|
| |
|||
| © 1999-2026 Южный математический институт | |||