Energy decay for Timoshenko systems of memory type

By F. Ammar-Khodja, Assia Benabdallah, J. E. Muñoz Rivera, Reinhard Racke. 2003

319 citations recorded by the source corpus.

Abstract Linear systems of Timoshenko type equations for beams including a memory term are studied. The exponential decay is proved for exponential kernels, while polynomial kernels are shown to lead to a polynomial decay. The optimality of the results is also investigated.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/35a2817efc6d40fe6aa5169e6590f96755f31f93

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In Computational Theory and Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Energy decay in a Timoshenko-type system of thermoelasticity of type III with different wave-propagation speeds (2013, background): “[1], Guesmia andMessaoudi [8,9], Messaoudi andMustafa [12,14] andMessaoudi et al.”
Timoshenko systems with indefinite damping (2008, background): “In the author’s paper [1] the damping aψt could be replaced by a memory term t ∫ 0 g(t− s)ψxxds, and in [14] by a coupling to a heat equation, see also [15] for nonlinear systems.”
On the Stability of Damped Timoshenko Systems: Cattaneo Versus Fourier Law (2009, background): “[1] for finite history), this means that the Fourier model of heat conduction preserves the exponential stability of the model, while the — still assumed to have a dissipative effect — Cattaneo model destabilizes in the sense that it is no longer exponentially stable.”
INDIRECT STABILIZATION OF LOCALLY COUPLED WAVE-TYPE SYSTEMS (2012, background): “One can show that polynomial stability holds through indirect mechanisms (see [8], [10] and the references therein) such as the ones considered in the present paper.”
Stability of Timoshenko systems with past history (2008, unknown): “Introducing non-zero history on ψ makes the problem different from that considered in [1], so different techniques have to be used.”
Bresse system with infinite memories (2015, unknown): “For more results concerning materials with ‘finite’ or ‘infinite’ memory, we refer to [16–19].”
Stability to weakly dissipative Timoshenko systems (2013, background): “[9] considered the memory effect, and Muñoz Rivera and Fernández Sare [10] treated the Timoshenko systems with a past history under suitable conditions on the relaxation functions.”
Global stability for damped Timoshenko systems (2003, methodology): “the common linear Timoshenko system, cf. [ 1 ], [8].”