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- W2525249663 abstract "In L 2 ( R d ; C n ) , we consider selfadjoint strongly elliptic second order differential operators A ε with periodic coefficients depending on x / ε . We study the behavior of the operator exp ( − i A ε τ ) , τ ∈ R , for small ε . Approximations for this exponential in the ( H s → L 2 ) -operator norm are obtained. The method is based on the scaling transformation, the Floquet–Bloch theory, and the analytic perturbation theory. The results are applied to study the behavior of the solution u ε of the Cauchy problem for the Schrödinger-type equation i ∂ τ u ε = A ε u ε + F . Applications to the nonstationary Schrödinger equation and the two-dimensional Pauli equation with singular rapidly oscillating potentials are given." @default.
- W2525249663 created "2016-10-07" @default.
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- W2525249663 date "2017-02-01" @default.
- W2525249663 modified "2023-09-29" @default.
- W2525249663 title "Spectral approach to homogenization of nonstationary Schrödinger-type equations" @default.
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- W2525249663 doi "https://doi.org/10.1016/j.jmaa.2016.09.037" @default.
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