Diffusion limit of a Boltzmann–Poisson system with nonlinear equilibrium state
2019 ◽
Vol 16
(01)
◽
pp. 131-156
Keyword(s):
The diffusion approximation for a Boltzmann–Poisson system is studied. Nonlinear relaxation type collision operator is considered. A relative entropy is used to prove useful [Formula: see text]-estimates for the weak solutions of the scaled Boltzmann equation (coupled to Poisson) and to prove the convergence of the solution toward the solution of a nonlinear diffusion equation coupled to Poisson. In one dimension, a hybrid Hilbert expansion and the contraction property of the operator allow to exhibit a convergence rate.
2004 ◽
Vol 55
(3)
◽
pp. 534-538
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Keyword(s):
1997 ◽
Vol 216
(2)
◽
pp. 593-613
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2021 ◽
Vol 10
(5)
◽
pp. 2611-2624
1990 ◽
Vol 43
(2)
◽
pp. 173-188
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Keyword(s):
2000 ◽
Vol 69
(4)
◽
pp. 985-986
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