In the field known as "the mathematical theory of shock waves," very exciting and unexpected developments have occurred in the last few years. Joel Smoller and

For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik,

. . . the progress of physics will to a large extent depend on the progress of nonlinear mathe matics, of methods to solve nonlinear equations . . . and therefo

Shock wave-boundary-layer interaction (SBLI) is a fundamental phenomenon in gas dynamics that is observed in many practical situations, ranging from transonic a