We consider solutions of the linear heat equation in RN with isolated singularities. It is assumed that the position of a singular point depends on time and is Hölder continuous with the exponent α∈(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∈(0,1/2]. It turns out that H=1/N is critical.
All Science Journal Classification (ASJC) codes
- Applied Mathematics