Exponential decay for the damped wave equation in unbounded domains

Nicolas Burq; Romain Joly

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arXiv · 1408.6054

Exponential decay for the damped wave equation in unbounded domains

Nicolas Burq·Romain Joly

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Abstract

We study the decay of the semigroup generated by the damped wave equation in an unbounded domain. We first prove under the natural geometric control condition the exponential decay of the semigroup. Then we prove under a weaker condition the logarithmic decay of the solutions (assuming that the initial data are smoother). As corollaries, we obtain several extensions of previous results of stabilisation and control.

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Nicolas Burq, Romain Joly. 2014-08-26. Exponential decay for the damped wave equation in unbounded domains. https://arxiv.org/abs/1408.6054

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