Smooth Localized Parametric Resonance for Wave Equations

This example is studied using Floquet theory. A classic example is k(t) = 1 + ε cosωt, where one finds regions of instability in the ε, ω plane for which there are solutions which grow exponentially in time. The instability regions are open and with closures touching ε = 0 at critical frequencies (see [A], [MW]). For any t, the constant coefficient problems with k frozen at k(t) is conservative and have no such growth.