IJPAM: Volume 59, No. 3 (2010)

EXPONENTIAL DECAY FOR THE TRANSMISSION PROBLEM
WITH TIME DEPENDENT COEFFICIENTS AND
LOCALIZED DAMPING

Eugenio Cabanillas$^1$, Juan B. Bernui$^2$, Zacarias Huaringa$^3$
$^{1,3}$Faculty of Mathematical Sciences
National University of San Marcos
Av. Universitaria, 1, Lima, PERU
$^1$e-mail: cleugenio@yahoo.com
$^3$e-mail: zhuaringas@unmsm.edu.pe
$^2$Faculty of Natural Sciences and Mathematics
National University of Callao
Lima, PERU
e-mail: jbernuib@yahoo.com


Abstract.In this paper we consider the nonlinear transmission problem for the wave equation with time dependent coefficients with localized interior damping. We prove that the energy of the system decays in an exponential decay rate to zero. We use multiplier techniques and suitable unique continuation lemma for the wave equation with variable coefficients to obtain the decay property.

Received: January 15, 2010

AMS Subject Classification: 35B40, 35L70, 45K05

Key Words and Phrases: transmission problem, time dependent coefficients, stability

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 59
Issue: 3