ASYMPTOTIC INTEGRATION OF A LINEAR PARABOLIC PROBLEM OF ARBITRARY ORDER WITH HIGH-FREQUENCY COEFFICIENTS IN THE CRITICAL CASE
For a linear parabolic problem of arbitrary order 2k (k Є N) with rapidly oscillating in time (high-frequency) lower coefficients and Dirichlet boundary conditions is proved the existence of a unique 2π/ω-periodic solution in time and a complete asymptotics of this time-periodic solution is constructed and justified. It is assumed that that own vectorvalued function a<sub>0</sub> corresponding to the zero eigenvalue does not have generalized vector-valued functions (with respect to Vishik-Lyusternik) with respect to a definite pair of operators A and B. The coefficient of the highest stationary operator is assumed to be degenerate: it has a simple zero proper value.