Asymptotics of the heat equation with `exotic' boundary conditions or with time dependent coefficients

TL;DR

This paper investigates the asymptotic behavior of the heat equation's solutions under various boundary conditions and with time-dependent coefficients, expanding understanding of heat trace and content asymptotics.

Contribution

It provides new asymptotic results for heat trace and content in complex boundary conditions and with time-dependent coefficients, broadening theoretical insights.

Findings

Derived heat trace asymptotics for exotic boundary conditions

Analyzed heat content asymptotics with time-dependent coefficients

Extended classical results to more general boundary scenarios

Abstract

The heat trace asymptotics are discussed for operators of Laplace type with Dirichlet, Robin, spectral, D/N, and transmittal boundary conditions. The heat content asymptotics are discussed for operators with time dependent coefficients and Dirichlet or Robin boundary conditions.