Parabolic Equations with Large Parameter. Inverse Problems

For an abstract parabolic equation with initial condition and multidimensional parabolic initial-boundary value problem with absolute terms rapidly oscillating in time, inverse problems of finding these absolute terms from some information about the partial asymptotics of the solutions of the original problems are stated and solved. In this case, the absolute terms are the products of two factors, one of which is described by a rapidly oscillating function (i.e., depends on fast time), while the second term may depend on ordinary time but does not depend on fast time. The following three cases are considered: where, in this pair, only one of the factors is known and where only the mean value of the rapidly oscillating factor is known.