The regularity and exponential decay of solution for a linear wave equation associated with two-point boundary conditions

TL;DR

This paper studies the existence, regularity, and decay properties of solutions to a linear wave equation with two-point boundary conditions, using Lyapunov functionals to establish exponential decay.

Contribution

It introduces a new approach to analyze the decay of solutions for wave equations with two-point boundary conditions through Lyapunov functionals.

Findings

Global solutions exist and are regular.

Solutions exhibit exponential decay over time.

Decay rate is characterized by a Lyapunov functional.

Abstract

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this problem by the construction of a suitable Lyapunov functional.