  An exponential Luenberger dynamical observer is proposed to estimate the
state of a general class of nonautonomous semilinear parabolic equations. The
result can be applied to the case where the output is given by state
measurements taken at a finite number of spatial points, that is, to the case
where our sensors are a finite number of delta distributions. The output
injection operator is explicit and the derivation of the main result involves
the decomposition of the state space into a direct sum of two oblique
components depending on the set of sensors. Simulations are presented as an
application to the Kuramoto--Sivashinsky models for flame propagation and fluid
flow.
