Comptes Rendus
no. 8
Partial differential equations
Finite dimensional global attractor for a suspension bridge problem with delay

Presented by: the Editorial Board

Salim A. Messaoudi1; Soh E. Mukiawa1; Enyi D. Cyril1
1 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 546, Dhahran 31261, Saudi Arabia
Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 808-824.

This paper is devoted to the study of a semilinear problem describing the downward displacement of a suspension bridge in the presence of a hanger restoring force h(u), an external force f which includes gravity, and a delay term which accounts for its history. The goal is to establish a well-posedness result and the existence of a finite-dimensional global attractor.

Cet article est consacré à l'étude d'un problème semi-linéaire décrivant le déplacement vers le bas d'un pont suspendu, en présence d'une force de rappel exercée par les câbles, une force extérieure qui tient compte de la gravité et un terme de retard qui représente l'historique.

Le but est d'établir un résultat bien posé et l'existence d'un attracteur global de dimension finie.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.05.014

Salim A. Messaoudi 1; Soh E. Mukiawa 1; Enyi D. Cyril 1

1 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 546, Dhahran 31261, Saudi Arabia 
@article{CRMATH_2016__354_8_808_0,
     author = {Salim A. Messaoudi and Soh E. Mukiawa and Enyi D. Cyril},
     title = {Finite dimensional global attractor for a suspension bridge problem with delay},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {808--824},
     publisher = {Elsevier},
     volume = {354},
     number = {8},
     year = {2016},
     doi = {10.1016/j.crma.2016.05.014},
     language = {en},
}
TY  - JOUR
AU  - Salim A. Messaoudi
AU  - Soh E. Mukiawa
AU  - Enyi D. Cyril
TI  - Finite dimensional global attractor for a suspension bridge problem with delay
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 808
EP  - 824
VL  - 354
IS  - 8
PB  - Elsevier
DO  - 10.1016/j.crma.2016.05.014
LA  - en
ID  - CRMATH_2016__354_8_808_0
ER  - 
%0 Journal Article
%A Salim A. Messaoudi
%A Soh E. Mukiawa
%A Enyi D. Cyril
%T Finite dimensional global attractor for a suspension bridge problem with delay
%J Comptes Rendus. Mathématique
%D 2016
%P 808-824
%V 354
%N 8
%I Elsevier
%R 10.1016/j.crma.2016.05.014
%G en
%F CRMATH_2016__354_8_808_0
Salim A. Messaoudi; Soh E. Mukiawa; Enyi D. Cyril. Finite dimensional global attractor for a suspension bridge problem with delay. Comptes Rendus. Mathématique, Volume 354 (2016) no. 8, pp. 808-824. doi : 10.1016/j.crma.2016.05.014. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.05.014/

[1] M. Al-Gwaiz; B. Vieri; F. Gazzola Bending and stretching energies in a rectangular plate modeling suspension bridges, Nonlinear Anal., Volume 106 (2014), pp. 18-34

[2] E. Berchio; A. Ferrero; F. Gazzola Structural instability of nonlinear plates modelling suspension bridges: mathematical answers to some long-standing questions, Nonlinear Anal., Real World Appl., Volume 28 (2016), pp. 91-125

[3] I. Chueshov; I. Lasiecka Long-Time Behaviour of Second Order Evolution Equations with Nonlinear Damping 195, vol. 12, Memoirs of the American Mathematical Society, Providence, RI, USA, 2008

[4] I. Chueshov; I. Lasiecka Von Karman Evolution Equations, Springer Verlag, 2012

[5] A. Ferrero; F. Gazzola A partially hinged rectangular plate as a model for suspension bridges, Discrete Contin. Dyn. Syst., Volume 35 (2015) no. 12, pp. 5879-5908

[6] F. Gazzola Mathematical Models for Suspension Bridges: Nonlinear Structural Instability, Modeling, Simulation and Applications, vol. 15, Springer Verlag, 2015

[7] F. Gazzola; Y. Wang Modeling suspension bridges through the Von Karman quasilinear plate equations (A.N. Carvalho; B. Ruf; E. Moreira dos Santos; J.-P. Gossez; S.H.M. Soares; T. Cazenave, eds.), Progress in Nonlinear Differential Equations and Their Applications, Contributions to Nonlinear Differential Equations and Systems, a Tribute to Djairo Guedes de Figueiredo on occasion of his 80th birthday, Birhäuser, 2015, pp. 269-297

[8] C.L. Navier Extraits des recherches sur la flexion des plans élastiques, Bull. Sci. Soc. Philom. Paris (1823), pp. 92-102

[9] S. Nicaise; C. Pignotti Stability and instability results of wave equation with a delay term in the boundary or internal feedback, SIAM J. Control Optim., Volume 45 (2006) no. 5, pp. 1561-1590

[10] S. Nicaise; C. Pignotti Stabilization of wave equation with boundary or internal distributed delay, Differ. Integral Equ., Volume 21 (2008) no. 9–10, pp. 935-958

[11] S. Nicaise; C. Pignotti; J. Valein Exponential stability of the wave equation with boundary time-varying delay, Discrete Contin. Dyn. Syst., Volume 4 (2011) no. 3, pp. 693-722

[12] A. Pazzy Semigroups of Linear Operators and Application to PDE, Applied Mathematical Sciences, vol. 44, Springer, 1983

[13] Y. Wang Finite time blow-up and global solutions for fourth order damped wave equations, J. Math. Anal. Appl., Volume 418 (2014) no. 2, pp. 713-733

Cited by Sources:

Comments - Policy