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Babich, P. V.; Levenshtam, V. B.; Prika, S. P.

Recovery of a rapidly oscillating source in the heat equation from solution asymptotics. (English. Russian original) Zbl 06864318

Comput. Math. Math. Phys. 57, No. 12, 1908-1918 (2017); translation from Zh. Vychisl. Mat. Mat. Fiz. 57, No. 12, 1955-1965 (2017).
Summary: 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.

Cited in 4 Documents

MSC:

35-XX Partial differential equations
74-XX Mechanics of deformable solids

Keywords:

heat equation; rapidly oscillating source; asymptotic expansion; inverse problem
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\textit{P. V. Babich} et al., Comput. Math. Math. Phys. 57, No. 12, 1908--1918 (2017; Zbl 06864318); translation from Zh. Vychisl. Mat. Mat. Fiz. 57, No. 12, 1955--1965 (2017)
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References:

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