Averaging principle and hyperbolic evolution equations

Details Averaging principle and hyperbolic evolution equations Averaging principle and hyperbolic evolution equations

2011-10-03

arxiv.org/abs/1110.0385v1

Mathematics

Analysis of PDEs

Scientific paper

An averaging principle is derived for the abstract nonlinear evolution equation where the almost periodic right hand-side is a continuous perturbation of the time-dependent family of linear operators determining a linear evolution system. It generalizes classical Henry's results for perturbations of sectorial operators on fractional spaces. It is also proved that the main hypothesis of the nonlinear averaging principle is satisfied for general hyperbolic evolution equations introduced by Kato.

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