Remark on the exponential decay of the solutions of the damped wave equation

TL;DR

This paper establishes a condition ensuring exponential decay of solutions to the damped wave equation and provides a method to compute the decay coefficient effectively.

Contribution

It introduces a new condition guaranteeing exponential decay and offers a practical method to compute the decay rate for the damped wave equation.

Findings

Proved a condition for exponential decay of solutions.

Developed a method for effective computation of decay coefficient.

Validated the decay condition through theoretical analysis.

Abstract

A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also presented.