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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2017, Volume 57, Number 12, Pages 1955–1965
DOI: https://doi.org/10.7868/S0044466917120079 (Mi zvmmf10648) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Recovery of a rapidly oscillating source in the heat equation from solution asymptotics

P. V. Babicha, V. B. Levenshtamab, S. P. Prikaa

a Vorovich Institute of Mathematics, Mechanics, and Computer Science, Southern Federal University, Rostov-on-Don, Russia
b Southern Institute of Mathematics, Vladikavkaz Scientific Center, Russian Academy of Sciences, Vladikavkaz, Russia
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DOI: https://doi.org/10.7868/S0044466917120079
Abstract: Four problems are solved in which a high-frequency source in the one-dimensional heat equation with homogeneous initial-boundary conditions is recovered from partial asymptotics of its solution. It is shown that the source can be completely recovered from an incomplete (two-term) asymptotic representation of the solution. The formulation of each source recovery problem is preceded by constructing and substantiating asymptotics of the solution to the original initial-boundary value problem.
Key words: heat equation, rapidly oscillating source, asymptotic expansion, inverse problem.
Received: 06.07.2016
Revised: 02.05.2017
English version:
Computational Mathematics and Mathematical Physics, 2017, Volume 57, Issue 12, Pages 1908–1918
DOI: https://doi.org/10.1134/S0965542517120065
Bibliographic databases:
Document Type: Article
UDC: 519.62
Language: Russian
Citation: P. V. Babich, V. B. Levenshtam, S. P. Prika, “Recovery of a rapidly oscillating source in the heat equation from solution asymptotics”, Zh. Vychisl. Mat. Mat. Fiz., 57:12 (2017), 1955–1965; Comput. Math. Math. Phys., 57:12 (2017), 1908–1918
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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