论文标题
热方程式中的孤立奇异性的行为就像分数布朗动作
Isolated singularities in the heat equation behaving like fractional Brownian motions
论文作者
论文摘要
我们考虑$ \ mathbb {r}^n $中线性热方程的解决方案，并具有孤立的奇异性。假定单数点的位置取决于时间，并且与指数$α\ in（0,1）$连续相关。我们表明，如果任何孤立的奇异性都比$α$弱的订单弱，则可以消除。我们还通过显示具有不可移动奇点的解决方案的存在来显示可移动性条件的最佳性。这些结果适用于奇异点的行为，就像赫斯特指数$ h \ in（0,1/2] $）的表现一样。事实证明$ h = 1/n $至关重要。
We consider solutions of the linear heat equation in $\mathbb{R}^N$ with isolated singularities. It is assumed that the position of a singular point depends on time and is Hölder continuous with the exponent $α\in (0,1)$. We show that any isolated singularity is removable if it is weaker than a certain order depending on $α$. We also show the optimality of the removability condition by showing the existence of a solution with a nonremovable singularity. These results are applied to the case where the singular point behaves like a fractional Brownian motion with the Hurst exponent $H \in (0,1/2] $. It turns out that $H=1/N$ is critical.
