Operator error estimates for homogenization of the nonstationary Schrödinger-type equations: sharpness of the results
Mark Aleksandrovich Dorodnyi · Applicable Analysis · 2021
In L2(Rd;Cn), we consider a self-adjoint matrix strongly elliptic second-order differential operator Aϵ with periodic coefficients depending on x/ϵ. We find approximations of the exponential e−iτAϵ, τ∈R, for small ε in the (Hs→L2)-operator norm with suitable s. The sharpness of the error estimates with respect to τ is discussed. The results are applied to study the behavior of the solution uϵ of the Cauchy problem for the Schrödinger-type equation i∂τuϵ=Aϵuϵ+F.