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Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given. This result...
Using probabilistic tools, this work states a pointwise convergence of
function solutions of the 2-dimensional Boltzmann equation to the function
solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of
Fournier (2000) on the Malliavin calculus for the Boltzmann
equation. Moreover, using the particle system introduced by Guérin and
Méléard (2003), some simulations of the solution of the Landau equation will be given. This result...
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