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As Jay Carr asked: What is a high speed stall?, Jan Hudec explained:
A difference from normal stall is that after supersonic flow separation the lift remains proportional to angle of attack and so the aircraft continues to behave more or less normally except for the change in trim.
This has leaded me to a question: Why doesn't Concorde stall?
The phenomena you are referring to is better known as "tuck". This is caused by buildup of a supersonic shock wave on the upper surface of an airfoil when a plane enters the transsonic Mach region of flight (approaching Mach 1). This leads to a disruption of airflow behind the shockwave, resulting in a pitching down even without excessive AOA. Concorde actually did this too, and trimmed for it with the help of fuel transfer pumps. Discovery of this effect in the 1940s also lead to the creation of the "all flying" horizontal stabilizer.
The designers gave Concorde a very long, pitch stable design, along with a delta wing. That, and 4 powerful Rolls Royce/Snecma 593 Olympus engines, easily pushed it past transsonic, cruising along at Mach 2 up to 60,000 feet.
"Normal" airliners simply are not designed for supersonic flight.
