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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.17769 |
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| _version_ | 1866908760610439168 |
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| author | Ishige, Kazuhiro Kawakami, Tatsuki Takada, Ryo |
| author_facet | Ishige, Kazuhiro Kawakami, Tatsuki Takada, Ryo |
| contents | We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces. Furthermore, we apply the real interpolation method in uniformly local Zygmund spaces to obtain sharp integral estimates on the inhomogeneous term and the nonlinear term. This enables us to find sharp sufficient conditions for the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_17769 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term Ishige, Kazuhiro Kawakami, Tatsuki Takada, Ryo Analysis of PDEs We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces. Furthermore, we apply the real interpolation method in uniformly local Zygmund spaces to obtain sharp integral estimates on the inhomogeneous term and the nonlinear term. This enables us to find sharp sufficient conditions for the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. |
| title | Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.17769 |