Isolated singularities in the heat equation behaving like fractional Brownian motions

被引：2

作者：

Fujii, Mikihiro ^{[1
]}

Okada, Izumi ^{[2
]}

Yanagida, Eiji ^{[3
]}

机构：

[1] Kyushu Univ, Grad Sch Math, Fukuoka 8190395, Japan

[2] Kyushu Univ, Fac Math, Fukuoka 8190395, Japan

[3] Tokyo Inst Technol, Dept Math, Meguro Ku, Tokyo 1528551, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 504卷 / 01期

关键词：

Removability; Isolated singularity; Heat equation; Fractional Brownian motion; TIME-DEPENDENT SINGULARITIES; REMOVABLE SINGULARITIES;

D O I：

10.1016/j.jmaa.2021.125322

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider solutions of the linear heat equation in R-N with isolated singularities. It is assumed that the position of a singular point depends on time and is Holder continuous with the exponent alpha is an element of (0, 1). We show that any isolated singularity is removable if it is weaker than a certain order depending on alpha. 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 is an element of (0,1/2]. It turns out that H = 1/N is critical. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：19

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