Bubbling singularities along a 2D heat flow with exponential nonlinearity

Abstract

Let $\Omega \subset {ℝ}^2$ be a smooth bounded domain. We consider solutions to the flow

where $u:\left[0,\infty \right)\times \Omega \to ℝ$ satisfies the Dirichlet boundary conditions and where the $L^1$-norm of $e^{u^2}$ is preserved. In this talk, we will describe the singularities arising potentially along this flow. (Joint work with T. Lamm and M. Struwe.)