Abstract
We consider in this article the monokinetic linear Boltzmann equation in two spacedimensions with degenerate cross section and produce,by means of a finite-volume method, numerical simulations of thelarge-time asymptotics of the solution.  The numerical computations are performed in the $2Dx-1Dv$ phase space onCartesian gridsand deal with both cross sections satisfyingthe geometrical condition and cross sections that do not satisfy it.  The numerical simulations confirm the theoretical results on the long-time behaviour of degenerate kinetic equationsfor cross sections satisfying the geometrical condition. Moreover, they suggest that, for general non-trivialdegenerate cross sections whose support contains a ball, the theoretical upper boundof order $t^{-1/2}$ for the time decay rate (in $L^2$-sense)can actually be reached.
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