Heat content asymptotics with singular data

TL;DR

This paper investigates the asymptotic behavior of heat content on manifolds with boundary under singular initial conditions, deriving the first three terms of the series and analyzing the interval case in detail.

Contribution

It provides the first detailed asymptotic expansion of heat content with singular data on manifolds, including explicit formulas for the initial terms.

Findings

First three terms of heat content asymptotics with singular data derived

Explicit formulas for the asymptotic coefficients obtained

Detailed analysis of the interval case included

Abstract

We study the asymptotic behaviour of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions. Assuming the existence of a complete asymptotic series we determine the first three terms in that series. In addition to the general setting, the interval is studied in detail.