摘要 : We study enhancement of diffusive mixing by fast incompressible time-periodic flows. The class of relaxation-enhancing flows that are especially efficient in speeding up mixing has been introduced in [2]. The relaxation-enhancing ... 展开 We study enhancement of diffusive mixing by fast incompressible time-periodic flows. The class of relaxation-enhancing flows that are especially efficient in speeding up mixing has been introduced in [2]. The relaxation-enhancing properry of a flow has been shown to be intimately related to the properties of the dynamical system it generates. In particular, time-independent flows u such that the operator u . del has sufficiently smooth eigenfunctions are not relaxation-enhancing. Here we extend results of [2] to time-periodic flows u (x, t) and, in particular, show that there exist flows such that for each fixed time the flow is Hamiltonian, but the resulting time-dependent flow is relaxation-enhancing. Thus we confirm the physical intuition that time dependence of a flow may aid mixing. We also provide an extension of our results to the case of a nonlinear diffusion model. The proofs are based on a general criterion for the decay of a sernigroup generated by an operator of the form Gamma + iAL(t) with a negative unbounded self-adjoint operator Gamma, a time-periodic self-adjoint operator-valued function L(t), and a parameter A >> 1. 收起