Criterion of the global solvability of regular and singular differential-algebraic equations

Abstract

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.