Lecture 15: Corner layers

So far we've been discussing boundary layers. But other kinds of layers (meaning regions of rapid variation in a function or its derivatives) can sometimes occur on the interior of a region. In this lecture and the next we'll look at examples of such interior layers. Our first example is a "corner layer" in which the solution y undergoes a rapid change in its derivative, creating a kink or "corner" that becomes increasingly sharp as the small parameter epsilon tends to zero. In the course of the analysis, we'll run into special functions called "parabolic cylinder functions" -- these arise in quantum mechanics, fluid dynamics, and many other parts of science and engineering.