Global unique solvability for nonlinear index-1 DAEs with monotonicity properties

Lennart Jansen , Michael Matthes , Caren Tischendorf

Preprint series: Journal of Differential Equations, 27

MSC 2000

34A09 Implicit equations, differential-algebraic equations

34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions

Abstract
Known solvability results for nonlinear index-1 differential-algebraic equations (DAEs) are in general local and rely on the Implicit Function Theorem. In this paper we derive a global result which guarantees unique solvability on a given time interval for a certain class of index-1 DAEs with certain monotonicity conditions. Such DAEs are of big interest in the analysis of partial differential-algebraic equations (PDAEs) when approximating solutions of PDAEs by solutions of DAEs. The nonlinear equations of the modified nodal analysis under the topological index-1 conditions fit into this class of DAEs and thus can be solved uniquely on any given time interval. Furthermore we investigate the behavior of the solution with respect to perturbations on the right hand side and in the initial value.