The heat flow with a critical exponential nonlinearity

We analyze the possible concentration behavior of heat flows related to the Moser–Trudinger energy and derive quantization results completely analogous to the quantization results for solutions of the corresponding elliptic equation. As an application of our results we obtain the existence of critical points of the Moser–Trudinger energy in a supercritical regime. © 2009 Elsevier Inc. All rights reserved