## Proceedings of the Japan Academy, Series A, Mathematical Sciences

- Proc. Japan Acad. Ser. A Math. Sci.
- Volume 85, Number 5 (2009), 61-66.

### On observability of parallel-flow diffusive heat exchanger equations with boundary output

Shin-ichi Nakagiri and Hideki Sano

#### 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.

#### Article information

**Source**

Proc. Japan Acad. Ser. A Math. Sci., Volume 85, Number 5 (2009), 61-66.

**Dates**

First available in Project Euclid: 29 April 2009

**Permanent link to this document**

https://projecteuclid.org/euclid.pja/1241018394

**Digital Object Identifier**

doi:10.3792/pjaa.85.61

**Mathematical Reviews number (MathSciNet)**

MR2527792

**Zentralblatt MATH identifier**

1170.93017

**Subjects**

Primary: 93C20: Systems governed by partial differential equations

Secondary: 93B07: Observability

**Keywords**

Parallel-flow heat exchanger equation boundary output observability $C_0-$ semigroup

#### Citation

Sano, Hideki; Nakagiri, Shin-ichi. On observability of parallel-flow diffusive heat exchanger equations with boundary output. Proc. Japan Acad. Ser. A Math. Sci. 85 (2009), no. 5, 61--66. doi:10.3792/pjaa.85.61. https://projecteuclid.org/euclid.pja/1241018394