Multisummability of formal solutions to the Cauchy problem for some linear partial differential equations |
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| Authors: | Hidetoshi Tahara Hiroshi Yamazawa |
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| Affiliation: | 1. Department of Information and Communication Sciences, Sophia University, Kioicho, Chiyoda-ku, Tokyo 102-8554, Japan;2. College of Engineer and Design, Shibaura Institute of Technology, Minuma-ku, Saitama-shi, Saitama 337-8570, Japan |
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| Abstract: | The paper considers the Cauchy problem for linear partial differential equations of non-Kowalevskian type in the complex domain. It is shown that if the Cauchy data are entire functions of a suitable order, the problem has a formal solution which is multisummable. The precise bound of the admissible order of entire functions is described in terms of the Newton polygon of the equation. |
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| Keywords: | primary, 35C10 secondary, 35A10, 35A20 |
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