Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Global existence and asymptotic behaviour of solutions for a class of fourth order strongly damped nonlinear wave equations


Authors: Xu Runzhang and Yang Yanbing
Journal: Quart. Appl. Math. 71 (2013), 401-415
MSC (2010): Primary 35L25, 35A01, 35L30
DOI: https://doi.org/10.1090/S0033-569X-2012-01295-6
Published electronically: October 23, 2012
MathSciNet review: 3112820
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Abstract: In this paper we study the initial boundary value problem for a class of fourth order strongly damped nonlinear wave equations $ u_{tt}-\Delta u+ \Delta ^2 u-\alpha \Delta u_t=f(u)$. By introducing a family of potential wells we prove the existence of global weak solutions and global strong solutions under some weak growth conditions on $ f(u)$. Furthermore we give the asymptotic behaviour of solutions.


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Additional Information

Xu Runzhang
Affiliation: College of Science, Harbin Engineering University, 150001, People’s Republic of China
Email: xurunzh@yahoo.com.cn

Yang Yanbing
Affiliation: College of Science, Harbin Engineering University, 150001, People’s Republic of China

DOI: https://doi.org/10.1090/S0033-569X-2012-01295-6
Keywords: Fourth order nonlinear wave equations, strong damping, global existence, asymptotic behaviour, potential well
Received by editor(s): May 27, 2011
Published electronically: October 23, 2012
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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