Time-averages of fast oscillatory systems, Discrete Contin

Abstract. Time-averages are common observables in analysis of experimental data and numerical simulations of physical systems. We describe a straight-forward framework for studying time-averages of dynamical systems whose solutions exhibit fast oscillatory behaviors. Time integration averages out the oscillatory part of the solution that is caused by the large skew-symmetric operator. Then, the time-average of the solution stays close to the kernel of this operator. The key assumption in this framework is that the inverse of the large operator is a bounded mapping between certain Hilbert spaces mod-ular the kernel of the operator itself. This assumption is verified for several examples of time-dependent PDEs. 1. Introduction. Time-averagin