Solution to the one-dimensional telegrapher's equation subject to a backreaction boundary condition

TL;DR

This paper derives Green's functions for the one-dimensional telegrapher's equation under radiation and backreaction boundary conditions, extending analytical solutions to include reaction effects in wave propagation models.

Contribution

It introduces a backreaction boundary condition for the telegrapher's equation and provides explicit Green's function solutions, expanding the analytical framework for reaction-diffusion systems.

Findings

Derived Green's function for radiation boundary condition

Formulated backreaction boundary condition for telegrapher's equation

Provided explicit solutions for reaction-influenced wave propagation

Abstract

We discuss solutions of the one-dimensional telegrapher's equation in the presence of boundary conditions. We revisit the case of a radiation boundary condition and obtain an alternative expression for the already known Green's function. Furthermore, we formulate a backreaction boundary condition, which has been widely used in the context of diffusion-controlled reversible reactions, for a one-dimensional telegrapher's equation and derive the corresponding Green's function.