IJPAM: Volume 59, No. 3 (2010)
EXPONENTIAL DECAY FOR THE TRANSMISSION PROBLEM
WITH TIME DEPENDENT COEFFICIENTS AND
LOCALIZED DAMPING
WITH TIME DEPENDENT COEFFICIENTS AND
LOCALIZED DAMPING
Eugenio Cabanillas
, Juan B. Bernui
, Zacarias Huaringa
Faculty of Mathematical Sciences
National University of San Marcos
Av. Universitaria, 1, Lima, PERU
e-mail: cleugenio@yahoo.com
e-mail: zhuaringas@unmsm.edu.pe
Faculty of Natural Sciences and Mathematics
National University of Callao
Lima, PERU
e-mail: jbernuib@yahoo.com




National University of San Marcos
Av. Universitaria, 1, Lima, PERU



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