Unconditional uniqueness of Hardy--Hénon parabolic equations on Herz spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917154447687680 |
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| author | Hatano, Naoya Ikeda, Masahiro |
| author_facet | Hatano, Naoya Ikeda, Masahiro |
| contents | In this paper, we introduce the unconditional uniqueness of solutions in Herz spaces for the Hardy--Hénon parabolic equation, which is a semilinear heat equation with a power-type weight in the nonlinear term $|x|^γ|u|^{α-1}u$. It is expected that the power-type weight in the nonlinear term can be effectively handled within Herz spaces. In fact, our result in Herz spaces $\dot{K}^s_{q,r}({\mathbb R}^n)$ relaxes the endpoint case $q=α$ and the large interpolation exponent case $r\ge q$ compared to previous results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_16711 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unconditional uniqueness of Hardy--Hénon parabolic equations on Herz spaces Hatano, Naoya Ikeda, Masahiro Analysis of PDEs In this paper, we introduce the unconditional uniqueness of solutions in Herz spaces for the Hardy--Hénon parabolic equation, which is a semilinear heat equation with a power-type weight in the nonlinear term $|x|^γ|u|^{α-1}u$. It is expected that the power-type weight in the nonlinear term can be effectively handled within Herz spaces. In fact, our result in Herz spaces $\dot{K}^s_{q,r}({\mathbb R}^n)$ relaxes the endpoint case $q=α$ and the large interpolation exponent case $r\ge q$ compared to previous results. |
| title | Unconditional uniqueness of Hardy--Hénon parabolic equations on Herz spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.16711 |