587 research outputs found
Interior feedback stabilization of wave equations with dynamic boundary delay
In this paper we consider an interior stabilization problem for the wave
equation with dynamic boundary delay.We prove some stability results under the
choice of damping operator. The proof of the main result is based on a
frequency domain method and combines a contradiction argument with the
multiplier technique to carry out a special analysis for the resolvent
Asymptotic stability and blow up for a semilinear damped wave equation with dynamic boundary conditions
In this paper we consider a multi-dimensional wave equation with dynamic
boundary conditions, related to the Kelvin-Voigt damping. Global existence and
asymptotic stability of solutions starting in a stable set are proved. Blow up
for solutions of the problem with linear dynamic boundary conditions with
initial data in the unstable set is also obtained
Asymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system
This paper shows how the so called von Kármán model can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term through a fourth order dispersive operator is added. Introducing damping mechanisms, the authors also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter k. As k → ∞, the authors obtain the damped von Kármán model with associated energy exponentially decaying to zero as well
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