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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
Posted:
September 22, 2005
MathSciNet review:
2219008
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Additional Information
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.
References
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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:
http://dx.doi.org/10.1090/S0002-9947-05-03791-8
PII:
S 0002-9947(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
Posted:
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 after
28 years from publication.
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