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                <term xml:lang="en">Hypocoercivity</term>
                <term xml:lang="en">spatial weight</term>
                <term xml:lang="en">optimal design of damping set</term>
                <term xml:lang="en">Goldstein-Taylor model</term>
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              <p>For hypocoercive linear kinetic equations we first formulate an optimisation problem on a spatially dependent jump rate in order to find the fastest decay rate of perturbations. In the Goldstein-Taylor model we show (i) that for a locally optimal jump rate the spectral gap is determined by multiple, possible degenerate, eigenvectors and (ii) that globally the fastest decay is obtained with a spatially homogeneous jump rate. Our proofs rely on a connection to damped wave equations and a relationship to the spectral theory of Schrödinger operators.</p>
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