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Global existence of weak solutions for a system of non‐linear Boltzmann equations in semiconductor physics
Author(s) -
Mustieles Francisco José
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.1670140205
Subject(s) - boltzmann equation , mathematics , regularization (linguistics) , compact space , semiconductor , boltzmann constant , distribution function , mathematical analysis , statistical physics , physics , quantum mechanics , artificial intelligence , computer science
In this paper we give a proof of the global existence of weak solutions for the semiconductor Boltzmann equation. This equation rules the evolution of the distribution function of carriers in the kinetic model of semiconductors. The main tool for the proof consists of a recent compactness result on velocity averages of solutions of transport equations. This result needs a L 2 ‐estimate of the electric field, which is obtained from the energy estimate, using the original regularization procedure of the problem, proposed in this paper.