# A remark on observability of the wave equation with moving boundary

Source: [A remark on observability of the wave equation with moving boundary](<https://www.sota2.com/research/paper/68fa52221e209131ce9787a5>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T04:59:46.367Z

Authors: K. Ammari, A. Bchatnia, K. El Mufti

Published: 2015-07-20T17:43:44.000Z

## Abstract

We deal with the wave equation with assigned moving boundary ($0\<x\<a(t)$) upon which Dirichlet or mixed boundary conditions are specified, here $a(t)$ is assumed to move slower than the light and periodically. Moreover $a$ is continuous, piecewise linear with two independent parameters. Our major concern will be an observation problem which is based measuring, at each $t\>0$ of the transverse velocity at $a(t)$. The key to the results is the use of a reduction theorem.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1507.05568>)

[PDF](<https://arxiv.org/pdf/1507.05568.pdf>)