Consistent initialization and perturbation analysis for abstract differential-algebraic equations
type: Item
instance of: scholarly article
title: Consistent initialization and perturbation analysis for abstract differential-algebraic equations
zbMATH Open document ID: 1167.34022
author: Timo Reis
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 2009-02-09T00:00:00Z
review text: The author studies differential algebraic equations of the form \[ Ex'=Ax+f, \] where \(E\) and \(A\) are infinite dimensional linear operators on certain Hilbert spaces. These equations are often called abstract differential algebraic equations (ADAEs) or, if they arise from coupling partial differential equation with classical differential equations and algebraic constraints, partial differential algebraic equations (PDAEs). One main result is a sufficient conditions for the consistency of an initial value. To check this condition it is assumed that the PDAE can be transformed into a certain decoupling form. Furthermore, the author shows the continuous dependence of solutions with respect to certain norms of the (consistent) initial values and the inhomogeneities. The results are then applied to an illustrative example of an electrical circuit with a transmission line. The paper is well structured and nicely written.
reviewed by: Stephan Trenn
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 35B30
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 94C05
zbMATH DE Number: 5503805
zbMATH Keywords: Abstract differential-algebraic equations
zbMATH Keywords: Infinite-dimensional linear systems theory
zbMATH Keywords: Consistent initialization
zbMATH Keywords: Perturbation analysis
zbMATH Keywords: Partial differential-algebraic equations
MaRDI profile type: Publication
full work available at URL: s00498-007-0013-9
OpenAlex ID: W2037741121
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DOI: 10.1007/S00498-007-0013-9
description: scientific article; zbMATH DE number 5503805