Cathleen Morawetz
Courant Institute, NYU
Mixed Equations and Some Linear Problems From Transonic
Flows
The study of mixed equations goes back to the work of Tricomi in 1923 but
became of much greater interest in the 1950s when the possibility of flying
close to the speed of sound arose and it was fully recognized that the governing
equation was of mixed type, elliptic where the flow was subsonic and hyperbolic
where it was supersonic.We shall outline some problems of well-posedness
including an application of Noether's conservation law theorem. Most of the talk
will be devoted to desired but somewhat anomalous theorems for a linear mixed
equation whose solutions would describe perturbations of smooth transonic flows.