Evolutionary Problems Involving Sturm-Liouville Operators

TL;DR

This paper explores evolutionary problems involving Sturm-Liouville operators, focusing on a (1+1)-dimensional hyperbolic PDE with impedance boundary conditions, extending previous methods to more general cases.

Contribution

It extends an existing approach to evolutionary problems to the (1+1)-dimensional case with Sturm-Liouville operators and impedance boundary conditions.

Findings

Demonstrates the applicability of the approach to hyperbolic PDEs with Sturm-Liouville operators.

Provides a framework for solving evolutionary problems with impedance boundary conditions.

Extends previous methods to more general evolutionary problems.

Abstract

The purpose of this paper is to further exemplify an approach to evolutionary problems originally developed in earlier works for a special case and later extended to more general evolutionary problems. We are here concerned with the $(1+1)$ -dimensional evolutionary case, which in a particular case results in a hyperbolic partial differential equation with a Sturm-Liouville type spatial operator constrained by an impedance type boundary condition.