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Degenerate hyperbolic equations with lower degree degeneracy


Authors: Qing Han and Yannan Liu
Journal: Proc. Amer. Math. Soc. 143 (2015), 567-580
MSC (2010): Primary 35L15, 35L80
DOI: https://doi.org/10.1090/S0002-9939-2014-12288-X
Published electronically: October 30, 2014
MathSciNet review: 3283645
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Abstract: We prove that the Cauchy problem of degenerate hyperbolic equations is well-posed if leading coefficients are degenerate at a low degree.


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Qing Han
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556 – and – Beijing International Center for Mathematical Research, Peking University, Beijing 100871, People’s Republic of China
Email: qhan@nd.edu, qhan@math.pku.edu.cn

Yannan Liu
Affiliation: Department of Mathematics, Beijing Technology and Business University, Beijing 100048, People’s Republic of China – and – Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: liuyn@th.btbu.edu.cn, Yannan.Liu.148@nd.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-12288-X
Received by editor(s): October 4, 2009
Received by editor(s) in revised form: January 26, 2013
Published electronically: October 30, 2014
Additional Notes: The first author acknowledges the support of NSF Grant DMS-1105321
The second author acknowledges the support of NSFC Grant 11201011, BNSF Grant 1132002 and the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions (CIT&TCD201304029)
The authors would like to thank the referees for many helpful suggestions.
Communicated by: Walter Craig
Article copyright: © Copyright 2014 American Mathematical Society