On the well-posedness of the cauchy problem and the mixed problem for some class of hyperbolic systems and equations with constant coefficients and characteristics of variable multiplicity

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We study the well-posedness of the mixed problem for hyperbolic equations with constant coefficients and with characteristics of variable multiplicity. We single out a class of higher-order hyperbolic operators with constant coefficients and with characteristics of variable multiplicity, for which we obtain a generalization of the Sakamoto conditions for the well-posedness of the mixed problem in L2.