BLOW-UP AND GLOBAL SOLVABILITY OF THE CAUCHY PROBLEM FOR A NONLINEAR TIMOSHENKO BEAM VIBRATION EQUATION

封面

如何引用文章

全文:

开放存取 开放存取
受限制的访问 ##reader.subscriptionAccessGranted##
受限制的访问 订阅或者付费存取

详细

For a nonlinear fourth-order partial differential equation modeling the propagation of flexural waves in a Timoshenko beam, the Cauchy problem is studied in the space of continuous functions defined on the entire real axis and having limits at infinity. The time interval of existence and uniqueness of the classical solution to an auxiliary Cauchy problem related to the original one is established, and an estimate for the norm of this local solution is provided. Conditions ensuring the connection between local classical solutions of the original and auxiliary Cauchy problems on a specific time interval are found. Sufficient conditions for extending the local classical solution of the Cauchy problem to a global one and for the blow-up of the solution to the nonlinear Timoshenko equation on a finite time interval are considered.

作者简介

Kh. Umarov

Academy of Sciences of the Chechen Republic; Chechen State Pedagogical University

Email: umarov50@mail.ru
Grozny, Russia

参考

  1. Ерофеев В.И., Кажаев В.В., Семерикова Н.П. Волны в стержнях. Дисперсия. Диссипация. Нелинейность. М.: Физматлит, 2002. 208 с.
  2. Dunford N., Schwartz J.T. Linear Operators. Part I: General Theory. N.Y.: Interscience, 1958. xiv + 858 p. Данфорд Н., Шварц Дж. Т. Линейные операторы. Общая теория. М.: Изд-во иностр. лит., 1962. 896 с.
  3. Полянин А. Д. Справочник по линейным уравнениям математической физики М.: Физматлит, 2001. 576 с.
  4. Bateman H., Erdelyi A. Higher transcendental functions. V. 2. New York: McGraw-Hill Book Company, 1953. 316 p.
  5. Бейтмен Г., Эрдейи А. Высшие трансцендентные функции. Т. 2. М.: Наука, 1966. 296 с.
  6. Кудрявцев Л.Д. Курс математического анализа. М.: Дрофа, Т. 2. 2003. 720 с.
  7. Bainov D., Simeonov P. Integral Inequalities and Applications. Kluwer Academ. Publ., 1992. 245 p.
  8. Кудрявцев Л.Д. Курс математического анализа. М.: Дрофа, Т. 1. 2006. 702 с.
  9. Benjamin T.B., Bona J.L., Mahony J.J., Model equations for long waves in nonlinear dispersive systems // Philos. Trans. R. Soc. London. 1972. V. 272. P. 47–78.
  10. Корпусов М.О., Свешников А.Г., Юшков Е.В. Методы теории разрушения решений нелинейных уравнений математической физики. М.: Физический фак-т МГУ, 2014. 364 с.

补充文件

附件文件
动作
1. JATS XML
下载

版权所有 © Russian Academy of Sciences, 2025