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

被引：6

作者：

Al-Mahdi, Adel M. ^{[1
,2
]}

Al-Gharabli, Mohammad M. ^{[1
,2
]}

Nour, Maher ^{[3
]}

Zahri, Mostafa ^{[4
,5
]}

机构：

[1] King Fahd Univ Petr & Minerals, Preparatory Year Program, Dhahran 31261, Saudi Arabia

[2] King Fahd Univ Petr & Minerals, Interdisciplinary Res Ctr Construct & Bldg Mat, Dhahran 31261, Saudi Arabia

[3] King Fahd Univ Petr & Minerals, DCC Math, Dhahran 31261, Saudi Arabia

[4] Univ Sharjah, Coll Sci, Dept Math, Res Grp MASEP, Sharjah, U Arab Emirates

[5] Univ Sharjah, Coll Sci, Dept Math, Res Grp BioInformat FG, Sharjah, U Arab Emirates

来源：

AIMS MATHEMATICS | 2022年 / 7卷 / 08期

关键词：

variable exponent; Lebesgue and Sobolev spaces; boundary feedback; viscoelasticity; relaxation functions; general decay; finite difference method; GLOBAL EXISTENCE; DECAY; SPACES;

D O I：

10.3934/math.2022842

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：15370 / 15401

页数：32

共 48 条

[1] A note on the boundary stabilization of a compactly coupled system of wave equations [J].