A note on Fisher information hypocoercive decay for the linear Boltzmann equation. (English) Zbl 1470.35251
The paper deals with the long-time convergence to equilibrium of the solution of a linear Boltzmann equation for a system of particles influenced by a potential close to be quadratic. The collision operator appearing at the right-hand side of the equation describes random collisions with other particles with Gaussian velocities. Two cases are taken into account: in the first one all the components of the velocity are refreshed, in the second one only one component per time. Smooth initial data are considered, and it is shown that the Fisher Information (which bounds from above the relative entropy) with respect to the stationary state converges exponentially fast to zero.
Reviewer: Giovanni Mascali (Arcavacata di Rende)
MSC:
| 35Q20 | Boltzmann equations |
| 35K99 | Parabolic equations and parabolic systems |
| 60J25 | Continuous-time Markov processes on general state spaces |
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