Session S12 - Delay and functional differential equations and applications

Wednesday, July 21, 20:20 ~ 20:55 UTC-3

Dynamics of a Lamé system featuring damping-vs-delay

To Fu Ma

University of Brasília, Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk we discuss the long-time dynamics of weakly dissipative elasticity systems delay effects on the velocity. This damping-vs-delay feature was firstly considered by Nicaise and Pignotti (2006) in the context of interior and boundary controllability for wave equations. Our objective is to establish the existence of a smooth finite dimensional global attractor, allowing nonlinearities of critical growth. The main difficulty is finding necessary arguments to show that the system is quasi-stable in the sense of Chueshov and Lasiecka.

References:

[1] S. Nicaise and C. Pignotti, Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks, SIAM J. Control Optim. 45 (2006) 1561-1585.

[2] I. Chueshov and I. Lasiecka, Von Karman Evolution Equations. Well-Posedness and Long-Time Dynamics, Springer Monographs in Mathematics, Springer, New York, 2010.

[3] T. F. Ma, J. G. Mesquita and P. N. Seminario-Huertas, Smooth dynamics of weakly damped Lamé systems with delay, SIAM J. Math. Anal. (to appear).

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