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Main Title: Spectra and leading directions for differential-algebraic equations
Author(s): Linh, Vu Hoang
Mehrmann, Volker
Type: Research Paper
Abstract: The state of the art in the spectral theory of linear time-varying differential-algebraic equations (DAEs) is surveyed. To characterize the asymptotic behavior and the growth rate of solutions, basic spectral notions such as Lyapunov- and Bohl exponents, and Sacker-Sell spectra are discussed. For DAEs in strangeness-free form, the results extend those for ordinary differential equations, but only under additional conditions. This has consequences concerning the boundedness of solutions of inhomogeneous equations. Also, linear subspaces of leading directions are characterized, which are associated with spectral intervals and which generalize eigenvectors and invariant subspaces as they are used in the linear time-invariant setting.
Subject(s): differential-algebraic equation
strangeness index
Lyapunov exponent
Bohl exponent
Sacker-Sell spectrum
exponential dichotomy
leading direction
Issue Date: 29-Aug-2011
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 65L07 Numerical investigation of stability of solutions
65L80 Methods for differential-algebraic equations
34D08 Characteristic and Lyapunov exponents
34D09 Dichotomy, trichotomy
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2011, 14
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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