On the relativistic heat equation in one space dimension

TL;DR

This paper investigates the relativistic heat equation in one dimension, establishing local regularity under certain initial conditions and introducing a numerical scheme to analyze solution behavior.

Contribution

It provides the first local regularity result for the relativistic heat equation and proposes a numerical scheme to study solution properties.

Findings

Proved local regularity for solutions with Lipschitz initial data.

Developed a numerical scheme capturing key solution features.

Enabled analysis of qualitative solution behavior.

Abstract

We study the relativistic heat equation in one space dimension. We prove a local regularity result when the initial datum is locally Lipschitz in its support. We propose a numerical scheme that captures the known features of the solutions and allows for analysing further properties of their qualitative behavior.