Existence of a Solution to a System of Partial Differential Algebraic Equations of Arbitrary Index

Abstract

We consider a linear nonstationary system of first order partial differential equations that is not resolved with respect to the derivatives and identically degenerates in the domain. Without using the change of variables, we construct the structural form whose set of solutions coincides with the set of solutions to the original system. We obtain the hyperbolicity conditions and conditions for the correctness of initial and boundary conditions. We establish the existence of solutions to the initial-boundary value problem for hyperbolic systems of differential algebraic equations.