Upon the concept of index of linear partial differential-algebraic equations

We consider linear evolutionary systems of partial differential equations with constant coefficients of general form. We suppose that the matrix of operators at the higher time derivative of the sought vector-function is degenerate. These systems are called partial differential-algebraic equations (DAEs). The index is the most important characteristic defining the structure complexity of these equations. We discuss the ways of approach to the definition of index for partial DAEs and some related questions.