Enviar artigo por via de e-mail Exact Solutions of a Nonlinear Equation Describing Blow-Up Instability in Self-Oscillatory Systems
- Autores: Aristov A.I.1,2
-
Afiliações:
- Faculty of Computational Mathematics and Cybernetics, Moscow State University
- Federal Research Center “Computer Science and Control,” Russian Academy of Sciences
- Edição: Volume 63, Nº 11 (2023)
- Páginas: 1850-1858
- Seção: Partial Differential Equations
- URL: https://rjonco.com/0044-4669/article/view/664949
- DOI: https://doi.org/10.31857/S0044466923110042
- EDN: https://elibrary.ru/CIMCNK
- ID: 664949
Citar
Acesso aberto
Acesso está concedido
Somente assinantes
Resumo
A nonclassical fourth-order partial differential equation describing blow-up instability in self-oscillatory systems is studied. Several classes of exact solutions of this equation are constructed. It is shown that these solutions include ones growing to infinity in a finite time, ones bounded globally in time, and ones bounded on any finite time interval, but not globally.
Palavras-chave
Sobre autores
A. Aristov
Faculty of Computational Mathematics and Cybernetics, Moscow State University; Federal Research Center “Computer Science and Control,” Russian Academy of Sciences
Autor responsável pela correspondência
Email: ai_aristov@mail.ru
119992, Moscow, Russia; 119333, Moscow, Russia
Bibliografia
- Рабинович М.И., Трубецков Д.И. Введение в теорию колебаний и волн. М.: Наука, 1984.
- Рабинович М.И. Автоколебания распределенных систем. Известия вузов. Радиофизика. 1974. Т. 17. № 4. С. 477–510.
- Корпусов М.О. Разрушение в неклассических нелокальных уравнениях. М.: URSS, 2010.
- Свешников А.Г., Альшин А.Б., Корпусов М.О., Плетнер Ю.Д. Линейные и нелинейные уравнения соболевского типа. М.: Физматлит, 2007.
- Hayashi N., Kaikina E., Naumkin P., Shishmarev I. Asymptotics for Dissipative Nonlinear Equations. Springer-Verlag. 2006. 564 c.
- Полянин А.Д., Зайцев В.Ф., Журов А.И. Методы решения нелинейных уравнений математической физики и механики. М.: Физматлит, 2005.
- Полянин А.Д., Зайцев В.Ф. Справочник по нелинейным уравнениям математической физики. М.: Физматлит, 2002.
- Аристов А.И. О точных решениях одного неклассического уравнения в частных производных // Ж. вычисл. матем. и матем. физ. 2015. Т. 55. № 11. С. 1870–1875.
- Аристов А.И. О точных решениях одного неклассического нелинейного уравнения четвертого порядка // Матем. заметки. 2019. Т. 105. Вып. 4. С. 506–517.
- Aristov I. Exact Solutions of Three Nonclassical Equations, and Their Construction with Maple System // Lobachevskii J. Mathematics. 2019. V. 40. № 7. P. 851–860.
- Aristov I., Kholomeeva A.A., Moiseev E.I. Application of the Painleve Test to a Nonlinear Partial Differential Equation // Lobachevskii J. Mathematics. 2022. V. 43. № 7. P. 1791–1794.
Arquivos suplementares
