The sensitivity problem is defined for feedback systems with plants described by linear partial differential operators having constant coefficients, in a bounded one-dimensional domain. there are also finitely many observation points and finitely many lumped feedback loops, and a finite number of disturbance inputs. The sensitivity problem is studied in detail for the heat equation, and comments are made about the linearized damped beam equation and the damped wave equation. It is shown that it is possible to reduce arbitrarily the sensitivity over any temporal frequency interval uniformly in the space domain (except for the undamped wave equation, where a limitation in the frequency interval is induced by the plant). This reduction may require a high-gain feedback around the points where the disturbances appear.