Journal Article10.1007/BF00251609
Asymptotic stability in viscoelasticity
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TL;DR: In this article, it was shown that the solutions of (1.1) are asymptotically stable provided that g(T) is a nonnegative, monotonic non-increasing and convex function such that
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Abstract: where p, c are positive constants and g(r is independent of x; u(x, t) has been assigned on [0, 1 ] x ( oo, 0]. In a recent paper [1] the author investigated the problem of asymptotic stability for a class of abstract integrodifferential equations in function space, and the results were then applied to viscoelasticity. It was established, for instance, that the solutions of (1.1) are asymptotically stable provided that g(T) is a nonnegative, monotonic non-increasing and convex function such that
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Citations
Benjamin–Bona–Mahony Equations with Memory and Rayleigh Friction
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Effect compensation of the presence of a time-dependent interior delay on the stabilization of the rotating disk-beam system
TL;DR: In this article, the authors investigate the compensation problem of the effect of the interior time-dependent delay on the stabilization of a rotating disk-beam system, and show that the presence of such proposed controls assures the exponential stability of the system, provided that some reasonable conditions on the angular velocity of the disk and delay are fulfilled.
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Well-posedness and energy decay for Timoshenko systems with discrete time delay under frictional damping and/or infinite memory in the displacement
Aissa Guesmia
- 30 Jun 2017
TL;DR: In this article, the authors considered a vibrating system of Timoshenko-type in a bounded one-dimensional domain with discrete time delay and complementary frictional damping and infinite memory controls all acting on the transversal displacement and showed that the system is well-posed in the sens of semigroup and that, under appropriate assumptions on the weights of the delay and the history data, the stability of the system holds in case of the equal-speed propagation as well as in the opposite case in spite of the presence of a discrete-time delay.
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