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Blow‐up phenomena in the model of a space charge stratification in semiconductors: analytical and numerical analysis
Author(s) -
Korpusov Maxim Olegovich,
Lukyanenko Dmitry V.,
Panin Alexander A.,
Yushkov Egor V.
Publication year - 2016
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.4142
Subject(s) - uniqueness , mathematics , sobolev space , boundary value problem , stratification (seeds) , mathematical analysis , a priori and a posteriori , initial value problem , semiconductor , exponential function , numerical analysis , space (punctuation) , physics , quantum mechanics , seed dormancy , philosophy , linguistics , botany , germination , epistemology , dormancy , biology
The initial‐boundary value problems for a Sobolev equation with exponential nonlinearities, classical, and nonclassical boundary conditions are considered. For this model, which describes processes in crystalline semiconductors, the blow‐up phenomena are studied. The sufficient blow‐up conditions and the blow‐up time are analyzed by the method of the test functions. This analytical a priori information is used in the numerical experiments, which are able to determine the process of the solution's blow‐up more accurately. The model derivation and some questions of local solvability and uniqueness are also discussed. Copyright © 2016 John Wiley & Sons, Ltd.