On linear hypocoercive BGK models

Abstract

We study hypocoercivity for a class of linear and linearized BGK models for discrete and continuous phase spaces. We develop methods for constructing entropy functionals that prove exponential rates of relaxation to equilibrium. Our strategies are based on the entropy and spectral methods, adapting Lyapunov's direct method (even for "infinite matrices" appearing for continuous phase spaces) to construct appropriate entropy functionals. Finally, we also prove local asymptotic stability of a nonlinear BGK model.

References in corpus (2)

• Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation
• Sharp entropy decay for hypocoercive and non-symmetric Fokker-Planck equations with linear drift

Cited by in corpus (6)

• On multi-dimensional hypocoercive BGK models
• Hypocoercivity and controllability in linear semi-dissipative Hamiltonian ODEs and DAEs
• On optimal decay estimates for ODEs and PDEs with modal decomposition
• Large time convergence of the non-homogeneous Goldstein-Taylor Equation
• Finding the jump rate for fastest decay in the Goldstein-Taylor model
• Hypocoercivity for a BGK model for gas mixtures