The wave equation with specular derivatives

TL;DR

This paper introduces specular derivatives and specular spaces to formulate and solve the wave equation and transport equation in one dimension, expanding the mathematical framework for these equations.

Contribution

The paper develops a new concept of specular derivatives and associated function spaces, enabling the formulation and solution of wave and transport equations with these derivatives.

Findings

Successfully constructed the wave and transport equations with specular derivatives

Introduced and characterized new specular function spaces

Provided solutions to these equations within the new framework

Abstract

In this paper, we construct the transport equation and the wave equation with specular derivatives and solve these equations in one-dimension. To solve these equations, we introduce new function spaces, which we term specular spaces, consisting of certain specularly differentiable functions.