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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.

MSC:

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