What was found
(CAN) DURING DESCENT, PASSING THROUGH FL 170 AT AROUND 270 KNOTS, THE CREW ATTEMPTED AN APU START THAT LEAD TO A CYAN "APU SHUTDOWN" CAS MESSAGE. THE CREW SWITCHED THE APU TO THE OFF POSITION WHICH CLEARED THE MESSAGE. APPROXIMATELY 3-4 MINUTES LATER, A SECOND START ATTEMPT WAS PERFORMED. AFTER A FEW SECONDS THE RPM HUNG AT AROUND 35-40 PERCENT AND THE CREW ABORTED THE START. AFTER LANDING, A THIRD, UNSUCCESSFUL APU START ATTEMPT WAS MADE WHICH WAS ALSO ABORTED. POST FLIGHT INSPECTION REVEALED FIRE/HEAT RELATED DAMAGE TO THE APU INLET DUCT AND TAILCONE.