Blow-up rate of solution to generalised Blasius equation

We identify the blow-up rate of a solution to a generalised Blasius equation, that we came across while studying a probabilistic model of "Poissonian burning" in Euclidean space. Our proof involves the study of the long-time behaviour of solutions to a Lotka--Volterra system.
Comment: 20 pages, 3 figures. Comments welcome!