Quantitative rates of convergence to equilibrium for the degenreate linear Boltzman equation on the Torus

[1] Kazuo Aoki and Fran¸ cois Golse. On the speed of approach to equilibrium for a colli- sionless gas. On the distribution of free path lengths for the periodic Lorentz gas.

In this article we have proved that the solution of the linear transport equation converges in the long time limit to its global equilibrium state at an exponential rate if and only

For the May sample of the Roche population, the following variables were analyzed: date on which the nest cycle started, body size, intensity of red throat coloration corrected

For a general class of linear collisional kinetic models in the torus, including in particular the linearized Boltzmann equation for hard spheres, the linearized Landau equation

However, the study of the non-linear Boltzmann equation for soft potentials without cut-off [ 20 ], and in particular the spectral analysis its linearised version (see for instance [

We prove by the entropy production method the exponential decay in time of the solution to the only steady state of the associated stationnary equation.. Keywords:

In particular, the following questions have been addressed regarding steady solutions of kinetic equations of the type (1.1): (1) Existence [15, 11], (2) Uniqueness in some

According to the interpreters, the style represents one side of the Quranic miracle that is why these interpretations applied to the Quranic style prodigy was a practical example