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arXiv · 2411.07639

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

Kana Minami·Taku Yanagisawa
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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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Kana Minami, Taku Yanagisawa. 2024-11-12. Long-time asymptotic profiles of the n-D heat equation and modified heat kernels. https://arxiv.org/abs/2411.07639

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