Alberto Bressan - Penn State University

Parabolic equations with nonlinear source terms may have solutions which become unbounded in finite time. In this talk I'll discuss some basic topics of interest in the mathematical analysis of these solutions, namely: - Proving that blow-up actually occurs. - Estimating the time and location of blow up. - Describing the asymptotic shape of the solution close to the blow-up point, in terms of a suitable rescaling of variables. In particular, I will show how the correct rescaling of variables can be obtained, starting from a special symmetry group of the equations.