Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Global existence and asymptotic behavior for a mildly degenerate Kirchhoff wave equation with boundary damping

Author: Qiong Zhang
Journal: Quart. Appl. Math. 70 (2012), 253-267
MSC (2010): Primary 35L80, 35B40
DOI: https://doi.org/10.1090/S0033-569X-2012-01281-0
Published electronically: February 3, 2012
MathSciNet review: 2953102
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Abstract: In this article a degenerate nonlinear dissipative wave equation of Kirchhoff type with nonlinear boundary damping is considered. We prove the existence, uniqueness and regularity of the global solution of the system when the initial data are small enough and the geometry of the domain satisfies suitable assumptions. We also obtain the polynomial decay property of the global solution.

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Additional Information

Qiong Zhang
Affiliation: Department of Mathematics, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China
Email: zhangqiong@bit.edu.cn, qiongzhg@gmail.com

DOI: https://doi.org/10.1090/S0033-569X-2012-01281-0
Keywords: Degenerate equation, Kirchhoff equation, boundary dissipation, global existence, polynomial decay.
Received by editor(s): May 4, 2010
Published electronically: February 3, 2012
Additional Notes: The work is supported by the NSF of China (60504001, 60974033), SRF for ROCS, SEM, China (20080732041).
Article copyright: © Copyright 2012 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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