The Perturbation and ADAE Index of a Degenerated Hyperbolic System
2009 (English)Article in journal (Refereed) Published
We consider a linear version of the zero Mach-number limit of the Euler equations of compressible fluid flow. This system turns out to be a coupled hyperbolic/parabolic equation with coupled, time-dependent boundary conditions. Using the theory of abstract differential-algebraic equations it is shown that the frozen coefficient system has ADAE index 1. Moreover, the much stronger result is proven that the system has time-perturbation index one and space-perturbation index two even in the case of time-dependent boundary conditions. The results are stated in terms of the original physical variables. The estimates agree well with numerical experiments.
Place, publisher, year, edition, pages
2009. Vol. 53, no 1-2, 103-127 p.
Differential-algebraic equations, partial differential-algebraic, equations, abstract differential-algebraic equations, perurbation index, differential-algebraic equations, unbounded control, operators
IdentifiersURN: urn:nbn:se:kth:diva-18189DOI: 10.1007/s00025-008-0304-6ISI: 000263489800008ScopusID: 2-s2.0-67650630298OAI: oai:DiVA.org:kth-18189DiVA: diva2:336235
QC 201005252010-08-052010-08-052010-12-22Bibliographically approved