Electronic Journal of Differential Equations,
Vol. 2006(2006), No. 53, pp. 1-16.

Title: Nonlinear transmission problem with a dissipative boundary
       condition of memory type
       
Authors: Doherty Andrade (Maringa  State Univ., Brazil)
         Luci Harue Fatori (Londrina  State Univ., Brazil)
	 Jaime E. Munoz Rivera (Lab. Nal. de Comp., Petropolis, Brazil)

Abstract: 
 We consider a differential equation that models a material
 consisting of two elastic components. One component is clamped
 while the other is in a viscoelastic fluid producing a
 dissipative mechanism on the boundary.
 So, we have a transmission problem with boundary damping condition
 of memory type. We prove the existence of a global solution
 and its uniformly decay to zero  as time approaches infinity.
 More specifically, the solution decays exponentially
 provided the relaxation function decays exponentially.
 
Submitted November 10, 2005. Published April 28, 2006.
Math Subject Classifications: 35B40, 35L70.
Key Words: Wave equation; asymptotic behavior; memory.