Existence and qualitative behavior of solutions of abstract differential-algebraic equations

Abstract differential-algebraic equations (ADAEs) of a semilinear type are studied. Theorems on the existence and uniqueness of solutions and the maximal interval of existence, on the global solvability of the ADAEs, the boundedness of solutions and the blow-up of solutions are presented. Previously, an ADAE is reduced to a system of explicit differential equations and algebraic equations by using projectors. The number of equations of the system depends on the index of the characteristic pencil of the ADAE. We consider the pencil of an arbitrarily high index.