On the existence of a solution to some mixed problems for linear differential-algebraic partial differential equations

In the paper we consider a linear differential-algebraic system of partial differential equations with special matrix coefficients. Two cases are investigated. The first case is when the system has a small index and a matrix at unknown vector-function in the canonical form is arbitrary. The second case is when the system has an arbitrary index, while a matrix at the small term in the canonical form has a triangular form. In both cases, using the method of characteristics and the method of successive approximations, we prove the existence of a unique classical solution of mixed problems for the considered differential-algebraic systems of partial differential equations.