On the summability of the formal solutions for some PDEs with irregular singularity |
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Authors: | Zhuangchu Luo Hua Chen Changgui Zhang |
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Institution: | 1. Institute of Mathematics, Wuhan University, Wuhan 430072, PR China;2. Laboratoire AGAT (UMR-CNRS 8524), UFR math., Université de Lille 1, cité scientifique, 59655 Villeneuve d''Ascq cedex, France |
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Abstract: | In this Note, we consider some classes of nonlinear partial differential equations with regular singularity with respect to t=0 and irregular one with respect to x=0. Our purpose is to establish a result which is similar to the k-summability property, known in the case of singular ordinary differential equations. We can prove that, except at most a countable set, the formal solution is Borel summable or k-summable with respect to x in all other directions. To cite this article: Z. Luo et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003). |
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