NUMERICAL SOLUTIONS FOR A TIMOSHENKO-TYPE SYSTEM WITH THERMOELASTICITY WITH SECOND SOUND

被引：2
作者：
Hamouda, Makram [1 ]
Bchatnia, Ahmed [2 ]
Ayadi, Mohamed Ali [3 ]
机构：
[1] Imam Abdulrahman Bin Faisal Univ, Dept Basic Sci, Preparatory Year & Supporting Studies, POB 1982, Dammam 34212, Saudi Arabia
[2] Univ Tunis El Manar, Fac Sci Tunis, Dept Math, UR Anal Nonlineaire & Geometrie UR13ES32, Manar 2, Tunis 2092, Tunisia
[3] ESPRIT Sch Engn, UR Anal Nonlineaire & Geometrie UR13ES32, 1,2 Rue Andre Ampere, El Ghazala 2083, Tunisia
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2021年 / 14卷 / 08期
关键词：
asymptotic stability; finite difference methods; stability and convergence of numerical methods; thermoelasticity; Timoshenko system; Asymptotic behavior of solutions; GLOBAL EXISTENCE; STABILIZATION; DECAY;
D O I：
10.3934/dcdss.2021001
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider in this article a nonlinear vibrating Timoshenko system with thermoelasticity with second sound. We first recall the results obtained in [2] concerning the well-posedness, the regularity of the solutions and the asymptotic behavior of the associated energy. Then, we use a fourth-order finite difference scheme to compute the numerical solutions and we prove its convergence. The energy decay in several cases, depending on the stability number mu, are numerically and theoretically studied.
引用
收藏
页码：2975 / 2992
页数：18
相关论文
共 22 条
[1]   Non-Uniform Decay of the Energy of some Dissipative Evolution Systems [J].
Ammari, Kais ;
Bchatnia, Ahmed ;
El Mufti, Karim .
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 2017, 36 (02) :239-251
[2]   General decay in a Timoshenko-type system with thermoelasticity with second sound [J].
Ayadi, Mohamed Ali ;
Bchatnia, Ahmed ;
Hamouda, Makram ;
Messaoudi, Salim .
ADVANCES IN NONLINEAR ANALYSIS, 2015, 4 (04) :263-284
[3]   Lower bound and optimality for a nonlinearly damped Timoshenko system with thermoelasticity [J].
Bchatnia, Ahmed ;
Chebbi, Sabrine ;
Hamouda, Makram ;
Soufyane, Abdelaziz .
ASYMPTOTIC ANALYSIS, 2019, 114 (1-2) :73-91
[4]   Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrodinger equations [J].
Gao, Zhen ;
Xie, Shusen .
APPLIED NUMERICAL MATHEMATICS, 2011, 61 (04) :593-614
[5]   General energy decay estimates of Timoshenko systems with frictional versus viscoelastic damping [J].
Guesmia, Aissa ;
Messaoudi, Salim A. .
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2009, 32 (16) :2102-2122
[6]   On the control of a viscoelastic damped Timoshenko-type system [J].
Guesmia, Aissa ;
Messaoudi, Salim A. .
APPLIED MATHEMATICS AND COMPUTATION, 2008, 206 (02) :589-597
[7]  
Hamouda, 2020, COMPUT APPL MATH, V39
[8]   A Fourth Order Finite Difference Method for the Good Boussinesq Equation [J].
Ismail, M. S. ;
Mosally, Farida .
ABSTRACT AND APPLIED ANALYSIS, 2014,
[9]   BOUNDARY CONTROL OF THE TIMOSHENKO BEAM [J].
KIM, JU ;
RENARDY, Y .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1987, 25 (06) :1417-1429
[10]  
Komornik V., 1994, EXACT CONTROLLABILIT
123