Long-time asymptotic profiles of the n-D heat equation and modified heat kernels

2024/11/12 by Minami, Kana, Yanagisawa, Taku
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.07639

Abstract

We construct a long-time asymptotic profile to the initial value problem of the n-dimensional heat equation. Specifically, we present a modified heat kernel as a long-time asymptotic profile which changes the mass, the center of mass and the variance of the n-dimensional heat kernel in accordance with the moments of the initial data.

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