Asymptotic behavior of the transmission Euler-Bernoulli plate and wave equation with a localized Kelvin-Voigt damping

Abstract

Let a fourth and a second order evolution equations be coupled via the interface by transmission conditions, and suppose that the first one is stabilized by a localized distributed feedback. What will then be the effect of such a partial stabilization on the decay of solutions at infinity? Is the behavior of the first component sufficient to stabilize the second one? The answer given in this paper is that sufficiently smooth solutions decay logarithmically at infinity even the feedback dissipation affects an arbitrarily small open subset of the interior. The method used, in this case, is based on a frequency method, and this by combining a contradiction argument with the Carleman estimates technique to carry out a special analysis for the resolvent.

arXiv comment20 pages, 1 figure; 2016, 21 (6) : 1757-1774

References in corpus (3)

• Stability of elastic transmission systems with a local Kelvin-Voigt damping
• Energy decay estimates of elastic transmission wave/beam systems with a local Kelvin-Voigt damping
• Remark on the pointwise stabilization of an elastic string equation

Cited by in corpus (5)

• Stabilization for the wave equation with singular Kelvin-Voigt damping
• Regularity and asymptotic behaviour for a damped plate-membrane transmission problem
• Stabilization for Euler-Bernoulli beam equation with a local degenerated Kelvin-Voigt damping
• Energy Decay of some boundary coupled systems involving wave$\backslash$ Euler-Bernoulli beam with one locally singular fractional Kelvin-Voigt damping
• Long-time asymptotics for a coupled thermoelastic plate-membrane system