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On the Cauchy problem of degenerate hyperbolic equations
Author(s):
Qing
Han;
Jia-Xing
Hong;
Chang-Shou
Lin
Journal:
Trans. Amer. Math. Soc.
358
(2006),
4021-4044.
MSC (2000):
Primary 35L15, 35L80
Posted:
September 22, 2005
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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.
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:
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
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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