On Asymptotics for the Solution of a Singularly Perturbed Parabolic Problem with a Multizone Internal Transition Layer

For a singularly perturbed parabolic equation with Neumann boundary conditions, we construct and substantiate asymptotics of a time-periodic solution possessing a multizone internal transition layer. Multizonality of the transition layer is caused by the fact that the degenerate equation has three n...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2018-06, Vol.58 (6), p.925-949
Main Author: Butuzov, V. F.
Format: Article
Language:English
Subjects:
Asymptotic properties
Boundary conditions
Computational Mathematics and Numerical Analysis
Decomposition
Mathematics
Mathematics and Statistics
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Summary:For a singularly perturbed parabolic equation with Neumann boundary conditions, we construct and substantiate asymptotics of a time-periodic solution possessing a multizone internal transition layer. Multizonality of the transition layer is caused by the fact that the degenerate equation has three nonintersecting roots, two of which are simple and the third one has multiplicity two. The asymptotic decomposition of the solution is qualitatively different from the well-known decomposition in the case when all the three roots of the degenerate equation are simple.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542518060040