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arXiv · 2512.16711

Unconditional uniqueness of Hardy--H\'enon parabolic equations on Herz spaces

Naoya Hatano·Masahiro Ikeda
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Abstract

In this paper, we introduce the unconditional uniqueness of solutions in Herz spaces for the Hardy--H\'enon parabolic equation, which is a semilinear heat equation with a power-type weight in the nonlinear term $|x|^\gamma|u|^{\alpha-1}u$. 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 $q=\alpha$ and the large interpolation exponent case $r\ge q$ compared to previous results.

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Naoya Hatano, Masahiro Ikeda. 2025-12-18. Unconditional uniqueness of Hardy--H\'enon parabolic equations on Herz spaces. https://arxiv.org/abs/2512.16711

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