A Generalized Interpolation Inequality and its Application to the Stabilization of Damped Equations
arXiv:1207.2030 · doi:10.1016/j.jde.2007.06.003
Abstract
In this paper, we establish a generalized H{ö}lder'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 models, we can give an explicit decay estimate for pointwise damping mechanisms supported on any strategic point.