Asymptotic behavior of Kawahara equation with memory effect

In this work, we are interested in a detailed qualitative analysis of the Kawahara equation, a model that has numerous physical motivations such as magneto-acoustic waves in a cold plasma and gravity waves on the surface of a heavy liquid. First, we design a feedback law, which combines a damping control and a finite memory term. Then, it is shown that the energy associated with this system exponentially decays.Comment: 20 pages. Comments are welcom

On the boundary stabilization of the KdV-KdV system with time-dependent delay

The boundary stabilization problem of the Boussinesq KdV-KdV type system is investigated in this paper. An appropriate boundary feedback law consisting of a linear combination of a damping mechanism and a delay term is designed. Then, first, considering time-varying delay feedback together with a smallness restriction on the length of the spatial domain and the initial data, we show that the problem under consideration is well-posed. The proof combines Kato's approach and the fixed-point argument. Last but not least, we prove that the energy of the linearized KdV-KdV system decays exponentially by employing the Lyapunov method.Comment: To appear Nonlinear Analysis: Real World Application

Theme 4 | Simulation et optimisation de systemes complexes

This paper deals with nonlinear feedback stabilization problem of a #exible beam clamped at a rigid body and free at the other end. We assume that there is no damping. The feedbacklaw proposed here consists of a nonlinear control torque applied to the rigid body and either a nonlinear boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends thelinear case studied by Laousy et al. to a more general class of controls. This new class of controls is in particular of the interest to be robust

Search for supersymmetry in events with large missing transverse momentum, jets, and at least one tau lepton in 20 fb−1 of √s= 8 TeV proton-proton collision data with the ATLAS detector

© 2014, The Author(s). A search for supersymmetry (SUSY) in events with large missing transverse momentum, jets, at least one hadronically decaying tau lepton and zero or one additional light leptons (electron/muon), has been performed using 20.3fb−1of proton-proton collision data at √ s= 8 TeV recorded with the ATLAS detector at the Large Hadron Collider. No excess above the Standard Model background expectation is observed in the various signal regions and 95% confidence level upper limits on the visible cross section for new phenomena are set. The results of the analysis are interpreted in several SUSY scenarios, significantly extending previous limits obtained in the same final states. In the framework of minimal gauge-mediated SUSY breaking models, values of the SUSY breaking scale Λ below 63 TeV are excluded, independently of tan β. Exclusion limits are also derived for an mSUGRA/CMSSM model, in both the R-parity-conserving and R-parity-violating case. A further interpretation is presented in a framework of natural gauge mediation, in which the gluino is assumed to be the only light coloured sparticle and gluino masses below 1090 GeV are excluded