Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

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
Published electronically: October 23, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2010): 35L25, 35A01, 35L30

Retrieve articles in all journals with MSC (2010): 35L25, 35A01, 35L30


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: http://dx.doi.org/10.1090/S0033-569X-2012-01295-6
PII: S 0033-569X(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.



Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2014 Brown University
Comments: qam-query@ams.org
AMS Website