Email this article Recovery of a Rapidly Oscillating Source in the Heat Equation from Solution Asymptotics
- Authors: Babich P.V.1, Levenshtam V.B.1,2, Prika S.P.1
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Affiliations:
- Vorovich Institute of Mathematics, Mechanics, and Computer Science
- Southern Institute of Mathematics, Vladikavkaz Scientific Center
- Issue: Vol 57, No 12 (2017)
- Pages: 1908-1918
- Section: Article
- URL: https://journal-vniispk.ru/0965-5425/article/view/179572
- DOI: https://doi.org/10.1134/S0965542517120065
- ID: 179572
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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.
About the authors
P. V. Babich
Vorovich Institute of Mathematics, Mechanics, and Computer Science
Author for correspondence.
Email: xblahblahc@gmail.com
Russian Federation, Rostov-on-Don, 344090
V. B. Levenshtam
Vorovich Institute of Mathematics, Mechanics, and Computer Science; Southern Institute of Mathematics, Vladikavkaz Scientific Center
Email: xblahblahc@gmail.com
Russian Federation, Rostov-on-Don, 344090; Vladikavkaz, 362027
S. P. Prika
Vorovich Institute of Mathematics, Mechanics, and Computer Science
Email: xblahblahc@gmail.com
Russian Federation, Rostov-on-Don, 344090
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