Work

Stability results of coupled wave models with locally memory in a past history framework via nonsmooth coefficients on the interface

Year: 2021

Type: article

Abstract: In this paper, we investigate the stabilization of a locally coupled wave equations with local viscoelastic damping of past history type acting only in one equation via non smooth coefficients. First, using a general criteria of Arendt–Batty, we prove the strong stability of our system. Second, using a frequency domain approach combined with the multiplier method, we establish the exponential stability of the solution if and only if the two waves have the same speed of propagation. In case of different speed propagation, we prove that the energy of our system decays polynomially with rate t−1. Finally, we show the lack of exponential stability if the speeds of wave propagation are different.

Source: Mathematical Methods in the Applied Sciences

DOI: 10.1002/mma.7235

Authors: Mohammad Akil, Haidar Badawi, Serge Nicaise, Ali Wehbe

Institutions: Le LAMA, Université Savoie Mont Blanc, Université Polytechnique Hauts-de-France, Lebanese University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W3080313161

FWCI: 1.598

Cites: 35

Cited by: 24

Related to: 10