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