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

Helge Dietert; Josephine Evans

doi:10.1007/s10955-022-02925-3

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arXiv · 2103.10064

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

Helge Dietert·Josephine Evans

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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 Schr{\"o}dinger operators.

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Helge Dietert, Josephine Evans. 2021-03-18. Finding the jump rate for fastest decay in the Goldstein-Taylor model. https://doi.org/10.1007/s10955-022-02925-3

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