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.