关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Energy decay for Timoshenko systems of memory type

http://www.im.ufrj.br/~rivera/Art_Pub/RackeR01.pdf

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

We consider hyperbolic Timoshenko-type vibrating systems that are coupled to a heat equation modeling an expectedly dissipative effect through heat conduction. While exponential stability under the Fourier law of heat conduction holds, it turns out that the coupling via the Cattaneo law does not yield an exponentially stable system. This seems to be the first example that a removal of the paradox of infinite propagation speed inherent in Fourier’s law by changing to the Cattaneo law causes a loss of the exponential stability property. Actually, for systems with history, the Fourier law keeps the exponential stability known for the pure Timoshenko system without heat conduction, but introducing the Cattaneo coupling even destroys this property.

/pdf/on-the-stability-of-damped-timoshenko-systems-cattaneo-4dd3c3jltp.pdf

On the stability of damped Timoshenko systems - Cattaneo versus Fourier law

We consider a nonlinear Timoshenko system as an initial-boundary value
problem in a one-dimensional
bounded domain. The system has a dissipative mechanism through
frictional damping being present
only in the equation for the rotation angle.
We first give an alternative proof for a sufficient and necessary
condition for exponential stability for
the linear case. Polynomial stability is proved in general. The global
existence of small, smooth solutions and the exponential stability is
investigated for the nonlinear case.

/pdf/global-stability-for-damped-timoshenko-systems-4nfkvhpfq6.pdf

Global stability for damped Timoshenko systems

Resume Dans cette Note on etudie la stabilisation de la poutre de Timoshenko. Pour ce faire on utilise une seule force de controle.

Stabilisation de la poutre de Timoshenko

We study the uniform stabilization of a Timoshenko beam by one control force. We prove that under, one locally distributed damping, the exponential stability for this system is assured if and only if the wave speeds are the same.

Uniform stabilization for the timoshenko beam by a locally distributed damping

Linear systems of porous-thermo-elasticity including a memory term in one dimension are studied. We establish an exponential and polynomial decay results.

Energy decay for Porous-thermo-elasticity systems of memory type

https://lmb.univ-fcomte.fr/IMG/pdf/farid_JMAA2007_Timoshenko.pdf

Stabilization of the nonuniform Timoshenko beam

The demand for high frequency surface acoustic wave devices for modern telecommunication applications imposes the development of devices able to answer the manufacturer requirements. The use of high velocity substrates for which a piezoelectric layer is required to excite and detect surface waves has been widely investigated and requires the implementation of accurate theoretical tools to identify the best combinations of material. The present paper proposes a mixed formulation combining finite element analysis with a boundary integral method to accurately simulate the capability of massive periodic interdigital transducers to excite and detect guided acoustic waves in layered media. The proposed model is exploited for different typical configurations.

Abdelaziz Soufyane

Papers

Stabilisation de la poutre de Timoshenko

Uniform stabilization for the timoshenko beam by a locally distributed damping

Energy decay for Porous-thermo-elasticity systems of memory type

Stabilization of the nonuniform Timoshenko beam

Simulations of surface acoustic wave devices built on stratified media using a mixed finite element/boundary integral formulation