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

Helge Dietert (1, 2) , Josephine Evans (3)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 Leipzig University / Universität Leipzig
3 WMI - Warwick Mathematics Institute

This note is about how the rate of decay for a simple kinetic model depends on the rate of the collision process. We study the Goldstein-Taylor model with spatially dependent jump rate and aim to find the form of jump rate which maximises the rate of convergence to equilibrium in L 2. We also perform a peturbative study, to understand the dependence of eigenvalues on the jump rate and show that local optimisers for the the spectral gap occur when the the spectral gap eigenvalue is of order greater than one.

Mots clés: Hypocoercivity; spatial weight; optimal design of damping set; Goldstein-Taylor model; wave equation

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Helge Dietert, Josephine Evans. Finding the jump rate for fastest decay in the Goldstein-Taylor model. 2021. ⟨hal-03171498v1⟩