Strong stability of the mono-tubular heat exchanger equation with output feedback

We investigate asymptotic behavior of the C0C0-semigroup T(t)T(t) associated with the mono-tubular heat exchanger equation with output feedback by a perturbation method. It is shown that T(t)T(t) is bounded if a constraint is satisfied by the parameters and the spatial distribution function. Further, applying the Arendt–Batty–Lyubich–Vu theorem, a criterion is established to judge strong stability of T(t)T(t).