Корректность задачи Коши для трехчленных дифференциально- операторных уравнений высших порядков

Abstract

he criteria are established for the correctness of the Cauchy problem for the equations y⁽²ⁿ⁾ + Ay⁽ⁿ⁾+ By=0, t ∈ [0,∞), where n > 1, А ,В are arbitrary commuting self-adjoint operators in a Hilbert space. For n = 2, the criterion is illustrated by using an example of the dynamic equation for exponentially stratified rotating compressible fluid.