Abstract
AbstractWe consider the fractional Klein–Gordon equation in one spatial dimension, subjected to a damping coefficient, which is non‐trivial and periodic, or more generally strictly positive on a periodic set. We show that the energy of the solution decays at the polynomial rate for and at some exponential rate when . Our approach is based on the asymptotic theory of C0 semigroups in which one can relate the decay rate of the energy in terms of the resolvent growth of the semigroup generator. The main technical result is a new observability estimate for the fractional Laplacian, which may be of independent interest.
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