Geodesic
Recovery of a rapidly oscillating source in the heat equation from solution asymptotics
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12, pp. 1955-1965

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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. 
@article{ZVMMF_2017_57_12_a2,
     author = {P. V. Babich and V. B. Levenshtam and S. P. Prika},
     title = {Recovery of a rapidly oscillating source in the heat equation from solution asymptotics},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1955--1965},
     publisher = {mathdoc},
     volume = {57},
     number = {12},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_12_a2/}
}
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P. V. Babich; V. B. Levenshtam; S. P. Prika. Recovery of a rapidly oscillating source in the heat equation from solution asymptotics. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 12, pp. 1955-1965. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_12_a2/