The stabilization of wave equations with moving boundary

TL;DR

This paper investigates the stabilization of wave equations with moving boundaries, analyzing energy behavior under various boundary conditions and establishing well-posedness and stabilization results for delayed boundary cases.

Contribution

It provides new insights into energy dynamics for wave equations with moving boundaries and introduces stabilization techniques for equations with time delay.

Findings

Energy can decrease, increase, or stay constant depending on boundary parameters.

Proved well-posedness of wave equations with moving boundary and time delay.

Established stabilization results for these equations.

Abstract

In this paper, we consider the stabilization of wave equations with moving boundary. First, we show the solution behaviour of wave equation with Neumann boundary conditions, that is, the energy of wave equation with mixed boundary conditions may decrease, increase or conserve depending on the different range of parameter. Second, we prove the wellposedness and stabilization for the wave equation with time delay and moving boundary.