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

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.