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.

[Liatlordofthedungeon]

Thank you for excellent lectures and also that you tuned down on aps. Btw your book "Infinite Powers" is absolute masterpiece!

[zhuangjiwang]

26:30, if (the first term is large), then Y\sim X and the match will fail since X\to\infty. Am I correct?

[ilovethesmellofdbranesinth]

I find it strange that we're doing perturbation theory (small epsilon) here but we needed to solve the epsilon = 1 (!) problem to get the inner solution. And in the end we get the inner solution solves the problem for all epsilon. I guess it's because this equation has scale invariance?