The perturbation and ADAE index of a degenerated hyperbolic system modelling a heat exchanger
Please always quote using this URN:urn:nbn:de:0296-matheon-3989
- The heat exchanger in a heat pump can be modelled by 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.
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| Author: | Timo Reis, Michael Hanke |
|---|---|
| URN: | urn:nbn:de:0296-matheon-3989 |
| Referee: | Volker Mehrmann |
| Document Type: | Preprint, Research Center Matheon |
| Language: | English |
| Date of first Publication: | 2007/06/20 |
| Release Date: | 2007/06/20 |
| Institute: | Technische Universität Berlin |
| MSC-Classification: | 34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A09 Implicit equations, differential-algebraic equations [See also 65L80] |
| 34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A30 Linear equations and systems, general | |
| 34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Gxx Differential equations in abstract spaces [See also 34Lxx, 37Kxx, 47Dxx, 47Hxx, 47Jxx, 58D25] / 34G10 Linear equations [See also 47D06, 47D09] | |
| 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Exx Equations and systems with constant coefficients [See also 35N05] / 35E20 General theory | |
| 93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Axx General / 93A10 General systems | |
| Preprint Number: | 394 |
