BOUNDARY VALUE PROBLEM FOR A THIRD-ORDER EQUATION WITH MULTIPLE CHARACTERISTICS
Keywords:
Boundary value problem, uniqueness, existence, integral equations, the contraction mapping principle.Abstract
In this article the author studied one boundary value problem for a third-order nonlinear equation with multiple characteristics. The unique solvability to the problem was proven. The uniqueness of the solution to the boundary value problem was proven by the method of energy. To prove the existence of a solution to this problem, an auxiliary problem was considered, for which the Green function was constructed. By solving an auxiliary problem, the original problem was reduced to a integral equation. The solvability of the integral equation was established using the contraction mapping principle.
Downloads
References
1. L. Cattabriga. Un problem al contorno per una equazione parabolica di ordin dispari. Amali della Souola Normale Superiore di Pisa a Matematicha. Seria III. Vol XIII. Fasc. II. 1959. – p.163 - 203.
2. Кorteweg D. J, de Vries G. On the change of form of long waves аdvancing in a rectangular channel, and on a new type of long stationary waves / /Phil. Mag. 1895. Vol. 39. p. 422 – 443.3. Jeffrey A, Kakutani T, Weak nonlinear dispersive waves. A discussion centered around the Korteweg-de-Vris equation //Siam. Rew. 1972. vol. 14. № 4.
4. V. I. Karpman. Nonlinear waves in dispersive media. M., Nauka,1973, p.176
5. Baranov V. B., Krasnobaev K. V. Hydrodynamic theory of space plasma //Moscow. "Science", 1977. p.~-176
6. W. Paxson, B-W. Shen. A KdV-SIR equation and its analytical solution: an application for COVID-19 data analisis. Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena. 2023. p.1-24.
7. Bubnov B. A., General boundary value problems for the Korteweg–de Vries equation in a bounded domain // Differential equations. 1979, Volume 15, Number 1, 26–31.
8. Cerpa E., Montoya C., Zhang B., Local exact controllability to the trajectories of the Korteweg–de Vries–Burgers equation on a bounded domain with mixed boundary conditions // Journal of Differential Equations. 268(2020), p.4945–4972 .
9. Charles Bu , A Modified Transitional Korteweg-De Vries Equation: Posed in the Quarter Plane // Journal of Applied Mathematics and Physics. Vol.12 No.7, July 2024.
10. T. D. Jurayev . Boundary value problems for equations of mixed and . mixedcomposite types. Uzbekistan, “Fan”, 1979, 236 p.
11. Abdinazarov S., General boundary value problems for a third-order equation with multiple characteristics // Differential Equations. 1981. Vol. XVII. No. 1. p.3-
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
License Terms of our Journal
