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A half‐space problem for a non‐linear Boltzmann equation arising in semiconductor statistics
Author(s) -
Poupaud F.
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140204
Subject(s) - mathematics , boltzmann equation , uniqueness , fermi–dirac statistics , maxwell–boltzmann distribution , mathematical analysis , space (punctuation) , distribution (mathematics) , mean free path , boundary (topology) , boundary value problem , electron , quantum mechanics , physics , linguistics , philosophy
In semiconductors the distributions of electrons satisfy a non‐linear Boltzmann–Vlasov equation. We consider the half‐space problem arising in the study of boundary layers when the mean free path tends to zero. We prove the existence and the uniqueness of the solution for any prescribed entering distribution. We establish that this solution tends towards a Fermi–Dirac distribution exponentially fast.