A Generalized Interpolation Inequality and its Application to the Stabilization of Damped Equations

Pascal Bégout (1, 2) , Soria Fernando (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LAP - Laboratoire Analyse et Probabilités
3 [e-mail]

In this paper, we establish a generalized Hölder's or interpolation inequality for weighted spaces in which the weights are non-necessarily homogeneous. We apply it to the stabilization of some damped wave-like evolution equations. This allows obtaining explicit decay rates for smooth solutions for more general classes of damping operators. In particular, for $1-d$ models, we can give an explicit decay estimate for pointwise damping mechanisms supported on any strategic point.

Mots clés: damped equations; damping control; generalized Hölder's inequality; interpolation inequality; stabilization

Domaines: Equations aux dérivées partielles [math.AP]; Mathématiques [math]

Pascal Bégout, Soria Fernando. A Generalized Interpolation Inequality and its Application to the Stabilization of Damped Equations. Journal of Differential Equations, 2007, 240 (2), pp.324-356. ⟨10.1016/j.jde.2007.06.003⟩. ⟨hal-00715831v2⟩