Stabilization of a viscoelastic wave equation with boundary damping and variable exponents: Theoretical and numerical study-Reference-Cited by-同舟云学术

Stabilization of a viscoelastic wave equation with boundary damping and variable exponents: Theoretical and numerical study

Published:2022 Issue:8 Volume:7 Page:15370-15401
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Al-Mahdi Adel M.¹²,Al-Gharabli Mohammad M.¹²,Nour Maher³,Zahri Mostafa⁴

Affiliation:

1. The Preparatory Year Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

2. The Interdisciplinary Research Center in Construction and Building Materials, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

3. DCC-Math, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

4. Department of Mathematics, College of Sciences, Research Groups MASEP and BioInformatics FG, University of Sharjah, Sharjah, United Arab Emirates

Abstract

<abstract><p>In this work, we consider a viscoelastic wave equation with boundary damping and variable exponents source term. The damping terms and variable exponents are localized on a portion of the boundary. We first, prove the existence of global solutions and then we establish optimal and general decay estimates depending on the relaxation function and the nature of the variable exponent nonlinearity. Finally, we run two numerical tests to demonstrate our theoretical decay results. This study generalizes and enhances existing literature results, and the acquired results are thus of significant importance when compared to previous literature results with constant or variable exponents in the domain.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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