On the Newton–Kantorovich Scheme for Evolutionary Equations

Abstract: We propose a constructive form of the Newton–Kantorovich method to obtain solutions for evolutionary equations with small nonlinearities. The construction is applicable to equations in non-Banach linear spaces. The paper presents only a sketch of the method, without specifying the norms involved and without giving necessary – details. © The Author(s) 2024.

Авторы
Dymov Andrey V. 1, 2, 3 , Kuksin Sergei B. 1, 3, 4, 5
Journal
Proceedings of the Steklov Institute of Mathematics
Номер выпуска
1
Язык
English
Страницы
70-77
Статус
Published
Ссылка
Внешняя ссылка
DOI
10.1134/S0081543824060063
Том
327
Год
2024
Организации
  • 1 Steklov Mathematical Institute of RAS, Moscow, Russian Federation
  • 2 HSE University, Moscow, Russian Federation
  • 3 RUDN University, Moscow, Moscow Oblast, Russian Federation
  • 4 Université Paris Cité, Paris, Ile-de-France, France
  • 5 Institute for Financial Studies, Shandong University, Jinan, Shandong, China
Ключевые слова
approximate propagators; evolutionary equations; KAM theory; Newton–Kantorovich scheme
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