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On the Cauchy problem of degenerate hyperbolic equations |
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| Authors: | Qing Han Jia-Xing Hong Chang-Shou Lin |
| Affiliation: | Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556 -- and -- Max-Planck Institute for Mathematics, Inselstr. 22 - 26, 04103 Leipzig, Germany ; Institute of Mathematics, Fudan University, Shanghai, People's Republic of China ; Department of Mathematics, National Chung-Cheng University, Ming-Hsiung, Chiayi, Taiwan |
| 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. |
| Keywords: | Degenerate hyperbolic equations Cauchy problems |
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