On the solution of the Heaviside - Klein - Gordon thermal equation for heat transport in graphene

TL;DR

This paper analyzes the Heaviside-Klein-Gordon thermal equation, revealing that heat transport in graphene involves both fast ballistic waves and slow diffusion, with implications for understanding thermal behavior at different timescales.

Contribution

It introduces a solution to the Heaviside-Klein-Gordon thermal equation demonstrating the coexistence of ballistic and diffusive heat transport in graphene.

Findings

Identification of fast thermal wave as ballistic heat transport

Demonstration of slow diffusion at large times

Application to heat transport in graphene

Abstract

We report studies of the solution of the Heaviside - Klein - Gordon thermal equation. As the result it is shown that the solution consists of two components: the fast thermal wave and slow diffusion for very large (compared to relaxation time) time period. We argue that the fast thermal wave can be recognized as the indication of the ballistic heat transport. As an example we consider the ballistic heat transport in graphene.