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.
Damped equations; Damping control; Generalized Hölder's inequality; Interpolation inequality; Stabilization;
Communication in Partial Differential Equations, vol. 240, n. 2, September 2007, pp. 324–356