On a Class of Diffusion-Aggregation Equations

Yuming Zhang

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arXiv · 1801.05543

On a Class of Diffusion-Aggregation Equations

Yuming Zhang

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Abstract

We investigate the diffusion-aggregation equations with degenerate diffusion $\Delta u^m$ and singular interaction kernel $\mathcal{K}_s = (-\Delta)^{-s}$ with $s\in(0,\frac{d}{2})$. We analyze the regime %($m>2-2s/d$, $d$ is the dimension) where the diffusive forces are stronger than the aggregation forces. In such regime, we show existence, uniform boundedness and H\"{o}lder regularity of solutions in the case that either $s>\frac{1}{2}$ or $m<2$. Uniqueness is proved for kernels with $s>1$.

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Yuming Zhang. 2018-01-17. On a Class of Diffusion-Aggregation Equations. https://arxiv.org/abs/1801.05543

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