Homogenization of nonstationary Schrödinger type equations with periodic coefficients

الأصل · EN

In L₂(Rᵈ;Cⁿ) we consider selfadjoint strongly elliptic second order differential operators Aε with periodic coefficients depending on x/ε. We study the behavior of the operator exponential (-i Aε τ), τ∈ R, for small ε. Approximations for this exponential in the (Hˢ→ L₂)-operator norm with a suitable s are obtained. The results are applied to study the behavior of the solution uε of the Cauchy problem for the Schrödinger type equation i ∂τuε = Aε uε.