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April 2009 On observability of parallel-flow diffusive heat exchanger equations with boundary output
Shin-ichi Nakagiri, Hideki Sano
Proc. Japan Acad. Ser. A Math. Sci. 85(5): 61-66 (April 2009). DOI: 10.3792/pjaa.85.61

Abstract

This paper is concerned with the observability problem of a parallel-flow two-fluid heat exchanger equation with diffusion term. First, the case where two fluid temperatures are measured at the outlet is considered. It is shown that the observed system with the measurements becomes observable on any interval of time through a concrete series expression of the solution. Next, the two cases where each one of two fluid temperatures is measured at the outlet are considered. It is also shown that the observed system with the only one measurement becomes observable on any interval of time except for the special cases of physical constants appearing in the equation. For the exceptional cases the unobservable subspace is finite dimensional and is characterized by using the eigenfunctions of heat equation with fluid transfer term.

Citation

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Shin-ichi Nakagiri. Hideki Sano. "On observability of parallel-flow diffusive heat exchanger equations with boundary output." Proc. Japan Acad. Ser. A Math. Sci. 85 (5) 61 - 66, April 2009. https://doi.org/10.3792/pjaa.85.61

Information

Published: April 2009
First available in Project Euclid: 29 April 2009

zbMATH: 1170.93017
MathSciNet: MR2527792
Digital Object Identifier: 10.3792/pjaa.85.61

Subjects:
Primary: 93C20
Secondary: 93B07

Rights: Copyright © 2009 The Japan Academy

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Vol.85 • No. 5 • April 2009
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