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Finding the jump rate for fastest decay in the Goldstein-Taylor model

Abstract : 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.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03171498
Contributor : Helge Dietert <>
Submitted on : Thursday, April 8, 2021 - 10:54:34 PM
Last modification on : Thursday, April 15, 2021 - 3:08:17 PM

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  • HAL Id : hal-03171498, version 3
  • ARXIV : 2103.10064

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Helge Dietert, Josephine Evans. Finding the jump rate for fastest decay in the Goldstein-Taylor model. 2021. ⟨hal-03171498v3⟩

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