Initial traces and solvability of porous medium equation with power nonlinearity
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912484818944000 |
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| author | Ishige, Kazuhiro Miyake, Nobuhito Sato, Ryuichi |
| author_facet | Ishige, Kazuhiro Miyake, Nobuhito Sato, Ryuichi |
| contents | In this paper we study qualitative properties of initial traces of solutions to the porous medium equation with power nonlinearity, and obtain necessary conditions for the existence of solutions to the corresponding Cauchy problem. Furthermore, we establish sharp sufficient conditions for the existence of solutions to the Cauchy problem using uniformly local Morrey spaces and their variations, and identify the optimal singularities of the initial data for the solvability of the Cauchy problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_11826 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Initial traces and solvability of porous medium equation with power nonlinearity Ishige, Kazuhiro Miyake, Nobuhito Sato, Ryuichi Analysis of PDEs 35K65, 35K15, 35B33 In this paper we study qualitative properties of initial traces of solutions to the porous medium equation with power nonlinearity, and obtain necessary conditions for the existence of solutions to the corresponding Cauchy problem. Furthermore, we establish sharp sufficient conditions for the existence of solutions to the Cauchy problem using uniformly local Morrey spaces and their variations, and identify the optimal singularities of the initial data for the solvability of the Cauchy problem. |
| title | Initial traces and solvability of porous medium equation with power nonlinearity |
| topic | Analysis of PDEs 35K65, 35K15, 35B33 |
| url | https://arxiv.org/abs/2507.11826 |