Exponential stability and exact controllability of a system of coupled wave equations by second‐order terms (via Laplacian) with only one non‐smooth local damping-Reference-Cited by-同舟云学术

Exponential stability and exact controllability of a system of coupled wave equations by second‐order terms (via Laplacian) with only one non‐smooth local damping

Published:2023-10-19 Issue: Volume: Page:
ISSN:0170-4214
Container-title:Mathematical Methods in the Applied Sciences
language:en
Short-container-title:Math Methods in App Sciences

Author:

Akil Mohammad¹^ORCID,Hajjej Zayd²

Affiliation:

1. Univ. Polytechnique Hauts‐de‐France, INSA Hauts‐de‐France, CERAMATHS‐Laboratoire de Matériaux Céramiques et de Mathématiques Valenciennes France

2. Department of Mathematics, College of Science King Saud University Riyadh Saudi Arabia

Abstract

The purpose of this work is to investigate the exponential stability of a second‐order coupled wave equations by Laplacian with one locally internal viscous damping. The strong stability is established by combining a unique continuation result and a Carleman estimate. Besides, the exponential stability is proved under (PMGC) condition on the damping region without any restriction on wave propagation speed (i.e., whether the two wave equations propagate at the same speed or not). The proof of this result relies on the frequency domain method combined with the multiplier techniques.

Publisher

Wiley

Subject

General Engineering,General Mathematics

Link

https://onlinelibrary.wiley.com/doi/pdf/10.1002/mma.9724

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