Time-Averaging under Fast Periodic Forcing of Parabolic Partial Differential Equations: Exponential Estimates

摘要

The phases of a large class of parabolic partial differential equations with rapid time-periodic forcing can be separated up to exponential small errors. The originally nonautonomous equation is transformed such that the nonautonomous terms are exponentially small in the period h of the forcing. This is a counterpart for partial differential equations of the theorem by A. Neishtadt (1984. J. Appl. Math. Mech. 48, 134-139) for ordinary differential equations. In our case the exponential rate depends on time t and the estimates have the form h exp(-c(t)h~(-1/3).