2015/12/25 by Ahmed Bchatnia, Bchatnia, Ahmed, Makram Hamouda +4
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #FOS: Mathematics #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations #Thermoelastic and Magnetoelastic Phenomena
paper · pdf · doi:10.48550/arxiv.1512.08006
openalex publication_date 2015/12/25 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
In this work, we consider a nonlinear vibrating Timoshenko system with\nthermoelasticity with second sound. We recall first the results of\nwell-posdness and regularity and the asymptotic behavior of the energy obtained\nin citeAyadi. Then, we use a fourth order finite difference scheme to\ncompute the numerical solutions and thus we show the energy decay in several\ncases depending on the stability number. R 'esum 'e : Dans ce travail, on\nconsid `ere le syst `eme de Timoshenko non-lin 'eaire avec\nThermo- 'elasticit 'e et deuxi `eme son. On rappelle d'abord les r 'esultats\nd'existence, de r 'egularit 'e et du comportement asymptotique de l' 'energie\nobtenus dans citeAyadi. Ensuite, on valide num 'eriquement ces r 'esultats\nth 'eoriques. Pour cela, on utilise une m 'ethode de diff 'erences finies\nd'ordre 4. Ainsi la solution num 'erique obtenue permet de valider la\nd 'ecroissance de l' 'energie dans plusieurs cas selon la valeur du param `etre\nde stabilit 'e.\n