On observability of parallel-flow diffusive heat exchanger equationswith boundary output

摘要

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 aremeasured at the outlet is considered. It is shown that the observed system with the measurementsbecomes 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 consid-ered. It is also shown that the observed system with the only one measurement becomes observableon 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 byusing the eigenfunctions of heat equation with fluid transfer term.