Decay for the Kelvin–Voigt damped wave equation: Piecewise smooth damping

Achieving Arbitrarily Large Decay in the Damped Wave Equation

is referred to as the decay rate associated with a. If a is to be introduced in order to absorb an initial disturbance then one naturally wishes to strike upon that a with the least possible (most negative) decay rate. The mathematical attraction here lies in the oftnoted fact that, with respect to damping, ‘more is not better.’ More precisely, for constant a, the decay rate is not a decreasing...

Exponential decay of solutions of a nonlinearly damped wave equation

The issue of stablity of solutions to nonlinear wave equations has been addressed by many authors. So many results concerning energy decay have been established. Here in this paper we consider the following nonlinearly damped wave equation utt −∆u+ a(1 + |ut|)ut = bu|u|p−2, a, b > 0, in a bounded domain and show that, for suitably chosen initial data, the energy of the solution decays exponenti...

Local decay for the damped wave equation in the energy space

Damping for the elastic wave equation

Résumé: Le but de ce projet est une investigation des techniques d’amortissement pour l’équation d’onde. Cette étude est intéressante tant du point de vue de la physique et que de l’analyse numérique. En effet l’amortissement apparâıt fréquemment dans les systèmes avec friction. Du point de vue mathématique, l’amortissement donne une meilleure régularité de l’équation élastique qui est importan...

Energy decay for the damped wave equation under a pressure condition

We establish the presence of a spectral gap near the real axis for the damped wave equation on a manifold with negative curvature. This results holds under a dynamical condition expressed by the negativity of a topological pressure with respect to the geodesic flow. As an application, we show an exponential decay of the energy for all initial data sufficiently regular. This decay is governed by...