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arXiv · 1207.2030

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

Pascal Bégout·Soria Fernando
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Abstract

In this paper, we establish a generalized H{\"o}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 $1-d$ models, we can give an explicit decay estimate for pointwise damping mechanisms supported on any strategic point.

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Pascal Bégout, Soria Fernando. 2012-07-09. A Generalized Interpolation Inequality and its Application to the Stabilization of Damped Equations. https://doi.org/10.1016/j.jde.2007.06.003

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