Inverse initial-boundary value problem for systems of quasilinear evolution equations of odd order
- Authors: Balashov O.S.1, Faminskii A.V.1
-
Affiliations:
- Российский университет дружбы народов
- Issue: Vol 71, No 1 (2025): Nonlocal and nonlinear problems
- Pages: 18-32
- Section: Articles
- URL: https://journals.rcsi.science/2413-3639/article/view/327837
- DOI: https://doi.org/10.22363/2413-3639-2025-71-1-18-32
- EDN: https://elibrary.ru/STIIBB
- ID: 327837
Cite item
Full Text
Abstract
An inverse initial-boundary value problem on a bounded interval for systems of quasilinear evolution equations of odd order is considered. Integral conditions are chosen as overdeterminations, and boundary functions and right-hand sides of equations of a special type are chosen as controls. Results on the existence and uniqueness of solutions for small initial data or a small time interval are established.
About the authors
O. S. Balashov
Российский университет дружбы народов
Author for correspondence.
Email: balashovos@s1238.ru
Москва, Россия
A. V. Faminskii
Российский университет дружбы народов
Email: faminskiy-av@pfur.ru
Москва, Россия
References
- Бесов О.В., Ильин В.П., Никольский С.М. Интегральные представления функций и теоремы вложения. -М.: Наука, 1996.
- Фаминский А.В. О задачах управляемости для уравнения Кортевега-де Фриза с интегральным переопределением// Дифф. уравн.-2019.- 55, № 1.-С. 123-133.
- Balashov O.S., Faminskii A.V. On direct and inverse problems for systems of odd-order quasilinear evolution equations// Eurasian Math. J.- 2024.- 15, № 4.-С. 33-53.
- Bona J.L., Cohen J., Wang G. Global well-posedness for a system of KdV-type equations with coupled quadratic nonlinearities// Nagoya Math. J.- 2014.- 215.-С. 67-149.
- Faminskii A.V. On inverse problems for odd-order quasilinear evolution equations with general nonlinearity// J. Math. Sci. (N.Y.). -2023.-271, № 3.-С. 281-299.
- Faminskii A.V., Martynov E.V. Inverse problems for the higher order nonlinear Schr¨odinger equation// J. Math. Sci. (N.Y.). -2023.-274, № 4.-С. 475-492.
- Lu S., Chen M., Lui Q. A nonlinear inverse problem of the Korteweg-de Vries equation// Bull. Math. Sci. -2019.- 9, № 3.- 1950014.
- Majda A.J., Biello J.A. The nonlinear interaction of barotropic and equatorial baroclinic Rossby waves// J. Atmos. Sci. -2003.- 60.-С. 1809-1821.
- Prilepko A.I., Orlovsky D.G., Vasin I.A. Methods for solving inverse problems in mathematical physics.- New York-Basel: Marcel Dekker Inc., 1999
Supplementary files
