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Four problems about recovery of a high-frequency source in the one-dimensionheat equation with homogeneous initial-boundary conditions by some informationabout partial asymptotic of its solution have solved. It is shown, that thesource can be completely recovered from a specific data about incomplete(two-terms) asymptotic of the solution. Before formulation of each problemabout recovery of a source, construction and justification of the asymptotic ofthe solution of original initial-boundary problem is given.

Recovery of a fast oscillating source in the heat equation by asymptotic of the solution