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On a system of equations of composite type in a multidimensional region

1. The study of multidimensional systems of composite type with variable coefficients has started with the works [1] —[4]. Earlier, in the works of Dzhuraev, special examples of multidimensional systems of differential equations of composite type with constant coefficients had been considered (see [5], where a bibliography can be found). Systems of composite type in a two-dimensional region can be studied fairly simply [6]. 2. Let Ω C R" be an open set of finite measure. We consider in QT = (0, Τ) χ Ω the system of differential equations