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A Class of Fourth Order Damped Wave Equations with Arbitrary Positive Initial Energy

Part of: Hyperbolic equations and systems Partial differential equations

Published online by Cambridge University Press:  14 September 2018

Yang Liu ,
Jia Mu  and
Yujuan Jiao
Yang Liu
Affiliation:
College of Mathematics, Sichuan University, Chengdu 610065, People's Republic of China (liuyangnufn@163.com) College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, People's Republic of China
Jia Mu
Affiliation:
College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, People's Republic of China
Yujuan Jiao
Affiliation:
College of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730124, People's Republic of China
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Abstract

In this paper, we study the initial boundary value problem for a class of fourth order damped wave equations with arbitrary positive initial energy. In the framework of the energy method, we further exploit the properties of the Nehari functional. Finally, the global existence and finite time blow-up of solutions are obtained.

Keywords

fourth order damped wave equationsglobal existencefinite time blow-uparbitrary positive initial energy

MSC classification

Primary: 35A01: Existence problems
Secondary: 35B44: Blow-up 35L35: Initial-boundary value problems for higher-order hyperbolic equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 62 , Issue 1 , February 2019 , pp. 165 - 178
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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