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.
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Notes
- 1.
An eigenvalue is defective if its geometric multiplicity is strictly less than its algebraic multiplicity.
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Acknowledgments
The second author (AA) was supported by the FWF-doctoral school “Dissipation and dispersion in non-linear partial differential equations”. The third author (EC) was partially supported by U.S. N.S.F. grant DMS 1501007.
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Achleitner, F., Arnold, A., Carlen, E.A. (2016). On Linear Hypocoercive BGK Models. In: Gonçalves, P., Soares, A. (eds) From Particle Systems to Partial Differential Equations III. Springer Proceedings in Mathematics & Statistics, vol 162. Springer, Cham. https://doi.org/10.1007/978-3-319-32144-8_1
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DOI: https://doi.org/10.1007/978-3-319-32144-8_1
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