SAMS Subject Classification Number: 23

The blow-up phenomenon in nonlinear evolution equations has been an active area of research for decades. In this talk we focus on a nonlinear diffusion equation, one which exhibits a point blow-up in finite time. One can distinguish the three stages of the evolution as before blow-up, at blow-up, and post blow-up. Much is known about the first, less about the second, and very little about the third. We discuss the various methods that can be brought to bear on each of these stages, including analytical appproximation methods such as perturbation theory as well as numerical approximation methods. (Joint work with Marco Fasondini and John King.)

Bio: Professor Weideman graduated from the University of the Free state in 1986, and occupied positions at that university and at Oregon State University, as well as visiting positions at MIT and the University of Utah. He is currently Distinguished Professor of Applied Mathematics at Stellenbosch University.