Mildly dissipative nonlinear Timoshenko systems—global existence and exponential stability☆

By J. E. Muñoz Rivera, Reinhard Racke. 2002

299 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Networks and Communications, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/223d9641489fbb85d68371ffabbff86f3397e002

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In Applied Mathematics

In Computer Networks and Communications

In Control and Systems Engineering

Citations in the corpus

Energy decay in a Timoshenko-type system of thermoelasticity of type III with different wave-propagation speeds (2008, result): “For Timenshinko systems in classical thermoelasticity, Rivera and Racke [13] considered ρ1φtt − σ(φx,ψ)x = 0 in (0,∞)× (0, L) ρ2ψtt − bψxx + k (φx + ψ) + γθx = 0 in (0,∞)× (0, L) ρ3θt − kθxx + γψtx = 0 in (0,∞)× (0, L) , (1.”
The stability number of the Timoshenko system with second sound (2012, background): “This was proved to memory viscoelastic constitutive laws in [1,3,4,6,8,12]; to thermoelastic constitutive laws with Fourier law and also to thermoelastic dissipation of type III in [10,12,23]; to Timoshenko system with boundary dissipation in [15,16] and also with locally distributed dissipation [18”
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.”
Stability of Timoshenko systems with past history (2008, unknown): “In [4] the same authors consider a dissipative Timoshenko system with a dissipation through a coupling to a heat equation, and they show exponential stability if and only if (1.”
On the Stability of Damped Timoshenko Systems: Cattaneo Versus Fourier Law (2009, background): “11) It was shown in [11] that for τ = 0, i.”
Stability to weakly dissipative Timoshenko systems (2013, background): “Muñoz Rivera and Racke [6] studied a linear case with dissipation a t .a > 0/, and Alabau-Boussouira [7] considered a nonlinear feedback force acting only in the equation for the rotational angle.”
On the stabilization of the Timoshenko system by a weak nonlinear dissipation (2009, background): “In addition, Muñoz Rivera and Racke [13] treated a nonlinear system with damping effect through heat conduction of the form 1utt − (ux , x )x = 0 in (0, L)×(0,+∞) 2 t t −b xx +K (ux + )+ x = 0 in (0, L)×(0,+∞) 3 t −K xx + xt = 0 in (0, L)×(0,+∞) where is the difference temperature.”