Heat content

TL;DR

This paper investigates the small-time asymptotic behavior of heat content with specific boundary conditions, providing explicit formulas for initial temperature blowup near boundaries.

Contribution

It offers a complete asymptotic expansion for heat content with Dirichlet or Robin conditions, including explicit geometric formulas for initial blowup scenarios.

Findings

Derived explicit formulas for the first terms of the asymptotic expansion.

Established the existence of a complete small-time asymptotic expansion.

Analyzed heat content with boundary blowup initial conditions.

Abstract

We study the heat content asymptotics with either Dirichlet or Robin boundary conditions where the initial temperature exhibits radial blowup near the boundary. We show that there is a complete small-time asymptotic expansion and give explicit geometrical formulas for the first few terms in the expansion.