Abstract: The long time behavior of solutions to linear PDEs with time-periodic coefficients arise naturally in the stability analysis of time-periodic solutions, for instance in channel and pipe flows with oscillatory walls or pressure gradients. Such problems also arise in Quantum Mechanics and many other areas– for instance in determining whether or not an oscillatory laser field will lead to ionization of hydrogen atom.
Until recently, the analytical methods for dealing with such problems have all been in the perturbative regime. In the presentation, a mathematically rigorous yet constructive approach to such problems is illustrated. This involves, among other techniques, a rigorous WKB approach to an infinite set of differential-difference equations.
This work involves collaborators O. Costin, J.L. Lebowitz and S.J. Cowley
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