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In this paper the explicit (closed form) solutions to several application-motivated parabolic problems are presented. The boundary stabilization problem is converted to a problem of solving a specific linear hyperbolic partial differential equation (PDE). This PDE is then solved for several particular cases. Closed loop solutions to the original parabolic problem are also found explicitly. Output feedback problem under boundary measurement is explicitly solved with both anti-collocated and collocated sensor/actuator locations. It is shown how closed form frequency domain compensators based on the closed form observers and controllers can be designed

Explicit state and output feedback boundary controllers for partial differential equations