A must be constant when . This is at the throat of the nozzle. In the subsonic region where the density decreases slower than the velocity increases so increases with increasing u . In that case the continuity equation can only be satisfied if A decreases along the flow. In the supersonic region where the density decreases faster than the velocity increases, so decreases with increasing velocity.
Continuity then requires that A increases along the flow.
These arguments can also be expressed differently. If A decreases along a stationary flow, the continuity equation requires that increases proportionally. For an accelerating flow this can only occur if increases with u , which requires . On the other hand, if A increases then must decrease proportionally. For an accelerating flow this occurs only when decreases faster than u increases, which is the case if .