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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the Cauchy problem of degenerate hyperbolic equations


Authors: Qing Han, Jia-Xing Hong and Chang-Shou Lin
Journal: Trans. Amer. Math. Soc. 358 (2006), 4021-4044
MSC (2000): Primary 35L15, 35L80
Published electronically: September 22, 2005
MathSciNet review: 2219008
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Abstract: In this paper, we study a class of degenerate hyperbolic equations and prove the existence of smooth solutions for Cauchy problems. The existence result is based on a priori estimates of Sobolev norms of solutions. Such estimates illustrate a loss of derivatives because of the degeneracy.


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Additional Information

Qing Han
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556 – and – Max-Planck Institute for Mathematics, Inselstr. 22 - 26, 04103 Leipzig, Germany
Email: qhan@nd.edu, qinghan@mis.mpg.de

Jia-Xing Hong
Affiliation: Institute of Mathematics, Fudan University, Shanghai, People’s Republic of China
Email: jxhong@fudan.ac.cn

Chang-Shou Lin
Affiliation: Department of Mathematics, National Chung-Cheng University, Ming-Hsiung, Chiayi, Taiwan
Email: cslin@math.ccu.edu.tw

DOI: https://doi.org/10.1090/S0002-9947-05-03791-8
Keywords: Degenerate hyperbolic equations, Cauchy problems
Received by editor(s): April 16, 2003
Received by editor(s) in revised form: June 21, 2004
Published electronically: September 22, 2005
Additional Notes: The first author was supported in part by an NSF grant and a Sloan research fellowship
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.