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Global Well-Posedness for a Class of Kirchhoff-Type Wave System
Joint Authors
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-18, 18 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-12-07
Country of Publication
Egypt
No. of Pages
18
Main Subjects
Abstract EN
In recent years, the small initial boundary value problem of the Kirchhoff-type wave system attracts many scholars’ attention.
However, the big initial boundary value problem is also a topic of theoretical significance.
In this paper, we devote oneself to the well-posedness of the Kirchhoff-type wave system under the big initial boundary conditions.
Combining the potential well method with an improved convex method, we establish a criterion for the well-posedness of the system with nonlinear source and dissipative and viscoelastic terms.
Based on the criteria, the energy of the system is divided into different levels.
For the subcritical case, we prove that there exist the global solutions when the initial value belongs to the stable set, while the finite time blow-up occurs when the initial value belongs to the unstable set.
For the supercritical case, we show that the corresponding solution blows up in a finite time if the initial value satisfies some given conditions.
American Psychological Association (APA)
Jiang, Xiaoli& Wang, Xiaofeng. 2017. Global Well-Posedness for a Class of Kirchhoff-Type Wave System. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-18.
https://search.emarefa.net/detail/BIM-1123065
Modern Language Association (MLA)
Jiang, Xiaoli& Wang, Xiaofeng. Global Well-Posedness for a Class of Kirchhoff-Type Wave System. Advances in Mathematical Physics No. 2017 (2017), pp.1-18.
https://search.emarefa.net/detail/BIM-1123065
American Medical Association (AMA)
Jiang, Xiaoli& Wang, Xiaofeng. Global Well-Posedness for a Class of Kirchhoff-Type Wave System. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-18.
https://search.emarefa.net/detail/BIM-1123065
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123065