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