Preprint 2014-03
Differential-algebraic equations from a functional-analytic viewpoint: a survey.
Roswitha März
Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 2014-03
MSC 2000:
Abstract: The purpose of this paper is to provide an overview on the state of the
art concerning functional-analytic properties associated with differential-algebraic equations (DAEs). We summarize the relevant literature and develop a basic theory of linear and nonlinear differential-algebraic operators. In particular, we consider Fredholm properties, normal solvability, generalized inverses, least squares solutions, splittings of regular linear differential-algebraic operators, bounded outer inverses, local solvability of equations with regular nonlinear differential-algebraic operators, Newton-Kantorovich iterations and regularizations of the ill-posed problems arising from higher-index operators.
101 pp.