Formal power series solutions with coefficients defined on shrinking discs for some partial differential equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908696882184192 |
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| author | Lastra, Alberto Michalik, Sławomir Suwińska, Maria |
| author_facet | Lastra, Alberto Michalik, Sławomir Suwińska, Maria |
| contents | In this paper conditions, under which an integro-differential operator is a linear automorphism, are provided. Alternatively, the problem can be considered in terms of existence of a unique formal power series solution for a linear Cauchy problem, where the coefficients of the solution are of a certain Gevrey order on progressively shrinking domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formal power series solutions with coefficients defined on shrinking discs for some partial differential equations Lastra, Alberto Michalik, Sławomir Suwińska, Maria Analysis of PDEs 35C10, 35G10 In this paper conditions, under which an integro-differential operator is a linear automorphism, are provided. Alternatively, the problem can be considered in terms of existence of a unique formal power series solution for a linear Cauchy problem, where the coefficients of the solution are of a certain Gevrey order on progressively shrinking domains. |
| title | Formal power series solutions with coefficients defined on shrinking discs for some partial differential equations |
| topic | Analysis of PDEs 35C10, 35G10 |
| url | https://arxiv.org/abs/2512.06470 |