IJPAM: Volume 2, No. 3 (2002)

VISCOUS DAMPING EXPONENTIAL AND
STRONG STABILIZABILITIES OF A PERIODIC
SYSTEM OF HYPERBOLIC EQUATIONS

Reza Sarhangi
Mathematics Dept.
Towson University
8000 York Road, Towson
MD 21252-0001, USA
e-mail: [email protected]


Abstract.This paper studies a periodic system of hyperbolic equations in a finite number of bounded domains in $\R^n$, $n\in N$, which are joined serially at interfaces such that the wave travelling within each of them can be transmitted to the others. It is shown that by applying the appropriate internal controllers in each of m domains, $m\in\N$, the energy of the system decays uniformly exponentially (exponential stability). Withdrawing the damping mechanism from any of these domains may results in losing exponential stability in general. However, in this case, we are able to establish strong stability for the system. Simulations axe presented to illustrate the analytical results.

Received: February 28, 2002

AMS Subject Classification: 35L10, 35L15, 35L20

Key Words and Phrases: periodic systems of hyperbolic equations, exponential stability, strong stability, viscous damping

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2002
Volume: 2
Issue: 3