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On Weak Solutions to the Non‐stationary van Roosbroeck's System with Discontinuous Permittivities
Author(s) -
Frehse J.,
Naumann J.
Publication year - 1997
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/(sici)1099-1476(19970525)20:8<689::aid-mma877>3.0.co;2-r
Subject(s) - mathematics , limit (mathematics) , bounded function , a priori and a posteriori , stationary solution , mathematical analysis , diffusion , weak solution , physics , quantum mechanics , philosophy , epistemology
In this paper we prove the existence of a weak solution to the non‐stationary drift–diffusion equations (van Roosbroeck's system) of semiconductor theory involving discontinuous permittivities. The proof is based on an approximation of these equations by a system with bounded non‐linearities, deriving a priori estimates on the approximate solutions and then carrying out the passage to limit. The discussion is completed by some regularity results for the weak solution under consideration. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd. Math. Meth. Appl. Sci., Vol. 20, 689–706 (1997).