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arXiv · 2607.19247

Well-posedness and global existence for Hardy--H\'{e}non parabolic equations in Herz spaces

Douadi Drihem
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Abstract

In this paper, we study the Hardy-H\'{e}non parabolic equation \begin{equation*} \partial_t u=\Delta u+a|x|^{-\gamma}|u|^{\beta}u, \qquad t>0,\; x\in\mathbb{R}^{n}\setminus\{0\}, \quad \beta>0,\; a\in\mathbb{R}, \end{equation*} under suitable assumptions on the parameter $\gamma$. We establish the local and global well-posedness of mild solutions in homogeneous Herz spaces.

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Douadi Drihem. 2026-07-21. Well-posedness and global existence for Hardy--H\'{e}non parabolic equations in Herz spaces. https://arxiv.org/abs/2607.19247

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