Remarks on the linear wave equation

TL;DR

This paper discusses fundamental properties of the linear wave equation, including solution existence, energy conservation, growth behavior, domain considerations, and solution representations.

Contribution

It provides insights into the theoretical aspects of the linear wave equation, clarifying solution properties and domain effects.

Findings

Existence and uniqueness of weak solutions established

Energy conservation properties analyzed

Solution behavior in different domain settings examined

Abstract

We make some remarks on the linear wave equation concerning the existence and uniqueness of weak solutions, satisfaction of the energy equation, growth properties of solutions, the passage from bounded to unbounded domains, and reconciliation of different representations of solutions.