Solvability of inhomogeneous fractional semilinear heat equations in Lorentz--Morrey spaces
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911388436267008 |
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| author | Oka, Yusuke |
| author_facet | Oka, Yusuke |
| contents | We study the Cauchy problem for the fractional semilinear heat equation with distributional inhomogeneous terms. By introducing the Lorentz--Morrey spaces, we overcome limitations of real interpolation in the classical local Morrey spaces and obtain a sharp integral estimate for the nonlinear term. Moreover, in terms of Besov-type spaces, we give necessary conditions and sufficient conditions on inhomogeneous terms for the local-in-time existence of solutions belonging to Lorentz--Morrey spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_16809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solvability of inhomogeneous fractional semilinear heat equations in Lorentz--Morrey spaces Oka, Yusuke Analysis of PDEs 35A01, 35K58, 35R11 We study the Cauchy problem for the fractional semilinear heat equation with distributional inhomogeneous terms. By introducing the Lorentz--Morrey spaces, we overcome limitations of real interpolation in the classical local Morrey spaces and obtain a sharp integral estimate for the nonlinear term. Moreover, in terms of Besov-type spaces, we give necessary conditions and sufficient conditions on inhomogeneous terms for the local-in-time existence of solutions belonging to Lorentz--Morrey spaces. |
| title | Solvability of inhomogeneous fractional semilinear heat equations in Lorentz--Morrey spaces |
| topic | Analysis of PDEs 35A01, 35K58, 35R11 |
| url | https://arxiv.org/abs/2509.16809 |