arXiv subjects

Amelie Rambaud

Publications and source records attributed to Amelie Rambaud.

3 recordsLinked to original sources

arXiv2015

Asymptotic behavior of an inhomogeneous flexible structure with Cattaneo type of thermal effect

We consider vibrations of an inhomogeneous flexible structure modeled by a $1$D viscoelastic equation with Kelvin-Voigt, coupled with an expected dissipative effect : heat conduction governed by Cattaneo's law (second sound). We establish the well-posedness of the system and we prove the stabilization to be exponential for one set of boundary conditions, and at least polynomial for another set of boundary conditions. Two different methods are used: the energy method and another more original, using the semigroup approach and studying the Resolvent of the system.

math.AP↗

arXiv2015

Stabilization of transverse vibrations of an inhomogeneous Euler- Bernoulli beam with a thermal effect

We consider an inhomogeneous Euler-Bernoulli (EB) beam of length $L$ clamped at both ends and subject to : an external frictional damping and a thermal effect (Fourier law). We prove the well-posedness of the model and analyze the behavior of the solution as $t \rightarrow + \infty.$ The existence is proved using semigroup theory, and the exponential stabilization of solutions is obtained considering multiplier technique. A numerical illustration of the energy decay is given, based on initial data close to a real physical experiment.

math.AP↗

arXiv2015

Exponential stability to the Bresse system with boundary dissipation conditions

We consider the Bresse model with three control boundary conditions. We prove the exponential stability of the system using the semigroup theory of linear operators and a result obtained by Prüss.

math.AP↗