Asymptotic analysis of linear parabolic problems with singularities

Asymptotic methods are used to investigate a second-order linear parabolic problem with lower order coefficients rapidly oscillating in time. The coefficient multiplying the principal stationary operator is assumed to be singular, i.e., it has a simple zero eigenvalue. Under certain additional conditions, the problem is proved to have a unique time-periodic solution and its complete asymptotic expansion is constructed and justified.