  For regular and nonregular (singular) semilinear differential-algebraic
equations (DAEs), we prove theorems on the existence and uniqueness of global
solutions and on the blow-up of solutions, which allow one to identify the sets
of initial values for which the initial value problem has global solutions
and/or for which solutions is blow-up in finite time, as well as the regions
that the solutions cannot leave. Together these theorems provide a criterion of
the global solvability of semilinear DAEs. As a consequence, we obtain
conditions for the global boundedness of solutions.
