  In this letter, we study the leader-synchronization problem for a class of
partial differential equations with boundary control and in-domain coupling. We
describe the problem in an abstract formulation and we specialize it to a
network of parabolic partial differential equations. We consider a setting in
which a subset of the followers is connected to the leader through a boundary
control, while interconnections among the followers are enforced by distributed
in-domain couplings. Sufficient conditions in the form of matrix inequalities
for the selection of the control parameters enforcing exponential
synchronization are given. Numerical simulations illustrate and corroborate the
theoretical findings.
