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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 1, Pages 74–88 (Mi zvmmf10136)  

Asymptotic analysis of linear parabolic problems with singularities

V. V. Gusachenkoa, V. B. Levenshtamab

a Southern Federal University, ul. Mil’chakova 8a, Rostov-on-Don, 344090, Russia
b Southern Institute of Mathematics, Vladikavkaz Scientific Center, Russian Academy of Sciences, ul. Markusa 22, Vladikavkaz, 362027, Russia

Abstract: Asymptotic methods are used to investigate a second-order linear parabolic problem with lower order coefficients rapidly oscillating in time. The coefficient multiplying the principal stationary operator is assumed to be singular, i.e., it has a simple zero eigenvalue. Under certain additional conditions, the problem is proved to have a unique time-periodic solution and its complete asymptotic expansion is constructed and justified.

Key words: linear parabolic problem, high-frequency time coefficients, singular limit problem, complete asymptotic expansion, algorithm for justifying asymptotics.

Funding Agency Grant Number
Russian Foundation for Basic Research 12-01-00402-а


DOI: https://doi.org/10.7868/S004446691501007X

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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:1, 71–84

Bibliographic databases:

UDC: 519.633
Received: 10.04.2014

Citation: V. V. Gusachenko, V. B. Levenshtam, “Asymptotic analysis of linear parabolic problems with singularities”, Zh. Vychisl. Mat. Mat. Fiz., 55:1 (2015), 74–88; Comput. Math. Math. Phys., 55:1 (2015), 71–84

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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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