Section B.8 Problem Sheet 8
Due 3 April at 4pm, either in class or in the pigeon hole in 4W.
Exercise 5.1.1 exists to get you thinking about the necessity of the hypothesis \(u\gt0\) in Theorem 5.1, while Exercise 5.1.2 gives you practice verifying this hypothesis. Variants of this exercise are a perennial favourite on exams, and the same goes for Exercise 5.1.3.
Exercise 5.1.4 is a straightforward chain rule calculation which explains how the nonlinear PDE (5.1) becomes the nonlinear ODE (5.2) when considering radially symmetric solutions. A corollary is that the Laplacian of a radially symmetric function is itself radially symmetric, a fact which has shown up in one form or another on at least one previous exam.
Please feel free to email me, or drop by office hours (Wednesdays 1:15–2:05 in 4W 1.12). I am also more than happy to meet one-on-one or in a small group.
