What was found
AT FL390, CABIN DOOR BEGAN TO SQUEAL. AT FL405, CABIN BEGAN TO CLIMB 1,500 TO 2,000 FPM. CREW REQUESTED LOWER ALTITUDE FROM LAX ATC BUT WERE DENIED. AT THAT POINT, CREW DECLARED AN EMERGENCY DUE TO INABILITY TO CONTROL CABIN PRESSURE. AIRCRAFT LANDED WITHOUT INCIDENT. CURRENTLY IN MX. DOOR SEAL FOUND TO HAVE SEVERE TEAR AND THE MOD VALVES HAVE A HIGH LEAK RATE. REPLACED THE FOLLOWING PARTS DUE TO SUSPECTED FAILURE: CABIN DOOR SEAL, LT 3 WAY VALVE, LT AND RT MIXING VALVE. F/T OF PRESSURIZATION SYSTEM NORMAL.