  We study a class of nonlinear hyperbolic partial differential equations with
boundary control. This class describes chemical reactions of the type ``$A \to$
product'' carried out in a plug flow reactor (PFR) in the presence of an inert
component. An isoperimetric optimal control problem with periodic boundary
conditions and input constraints is formulated for the considered mathematical
model in order to maximize the mean amount of product over the period. For the
single-input system, the optimality of a bang-bang control strategy is proved
in the class of bounded measurable inputs. The case of controlled flow rate
input is also analyzed by exploiting the method of characteristics. A case
study is performed to illustrate the performance of the reaction model under
different control strategies.
