Abstract:We construct solutions of the fast diffusion equation, which exist for all $t\in \mathbb {R}$ and are singular on the set $\Gamma (t)≔\{ \xi (s) ; -\infty <s \leq ct \}$, $c>0$, where $\xi \in C^3(\mathbb {R};\mathbb {R}^n)$, $n\geq 2$. We also give a precise description of the behavior of the solutions near $\Gamma (t)$.

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中文翻译：

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快速扩散方程的蛇形奇点解

摘要：我们构造了快速扩散方程的解，它存在于所有 $t\in \mathbb {R}$ 并且在集合 $\Gamma (t)≔\{ \xi (s) ; -\infty <s \leq ct \}$, $c>0$, 其中 $\xi \in C^3(\mathbb {R};\mathbb {R}^n)$, $n\geq 2$ . 我们还给出了 $\Gamma (t)$ 附近解的行为的精确描述。

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