We study in an abstract setting the indirect stabilization of systems of two wave-like equations coupled by a localized zero order term. Only one of the two equations is directly damped. The main novelty in this paper is that the coupling operator is not assumed to be coercive in the underlying space. We show that the energy of smooth solutions of these systems decays polynomially at infinity, ...

The spectral and modal properties of the vocal tract are important acoustic characteristics since they take part in generating the formants of individual vowels. The positions of vowel formants on the spectrum frequency axis are mainly determined by the parameters and properties of the vocal tract : its size and geometry, boundary conditions ( opening mouth and glottis, closing ) and absorption...

In the present article, we consider a thermoelastic plate of Reissner-Mindlin-Timoshenko type with the hyperbolic heat conduction arising from Cattaneo’s law. In the absense of any additional mechanical dissipations, the system is often not even strongly stable unless restricted to the rotationally symmetric case, etc. We present a well-posedness result for the linear problem under general mixe...

This paper generalizes the Time Domain Passivity Control concept originally introduced by J.-H. Ryu et al. (2004) in order to work for multi-degree of freedom (DoF) haptic systems with time delay. Its energy computation (named passivity observer) factors in the phase shift caused by time delay, and is improved by an energy estimation. Moreover, the variable damping of the passivity controller i...

Abstract. We consider a damped linear wave equation defined on a bi-dimensional domain Ω. Due to the damping term defined on the sub-domain ω ⊂ Ω, the system is dissipative. We address the problem of the optimal position and shape design of the support ω in order to minimize the energy of the system at a given time T . Introducing an adjoint problem we first obtain explicitly the (shape) deriva...

In this note, we show how to marginalize over the damping parameter of the PageRank equation so as to obtain a parameter-free version known as TotalRank. Our discussion is meant as a reference and intended to provide a guided tour towards an interesting result that has applications in information retrieval and classification.

In this paper we construct the time dependent boundary states describing the “rolling D-brane solutions” in the NS5 background discovered recently by Kutasov by means of the classical DBI analysis. We first survey some aspects of non-compact branes in the NS5 background based on known boundary states in the N = 2 Liouville theory. We consider two types of non-compact branes, one of which is BPS...

We investigate the finite-time stabilization of a tree-shaped network of strings. Transparent boundary conditions are applied at all the external nodes. At any internal node, in addition to the usual continuity conditions, a modified Kirchhoff law incorporating a damping term αut with a coefficient α that may depend on the node is considered. We show that for a convenient choice of the sequence...

A novel multigrid method for the solution of the steady Reynolds-averaged Navier–Stokes equations is presented, that gives convergence speeds similar to laminar flow multigrid solvers. The method is applied to Menter’s one-equation turbulence model. New aspects of the method are the combination of nonlinear Gauss–Seidel smoothing on the finest grid with linear coarse-grid corrections, and local...

Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources" (2015). This paper investigates a quasilinear wave equation with Kelvin-Voigt damping, u t t − ∆ p u − ∆u t = f (u), in a bounded domain Ω ⊂ R 3 and subject to Dirichlét boundary conditions. The operator ∆ p , 2 < p < 3, denotes the classical p-Laplacian. The nonlinear term f (u) is a source feedback t...