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