Blow‐up phenomena in the model of a space charge stratification in semiconductors: analytical and numerical analysis

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 an...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2017-05, Vol.40 (7), p.2336-2346
Main Authors: Korpusov, Maxim Olegovich, Lukyanenko, Dmitry V., Panin, Alexander A., Yushkov, Egor V.
Format: Article
Language:English
Subjects:
blow‐up phenomena
Boundary value problems
contracting mapping
Crystal structure
Derivation
Initial value problems
local solvability
Mathematical analysis
Mathematical models
numerical blow‐up diagnostics
Semiconductors
test functions
Uniqueness
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4142