PDE Seminar Abstracts

Bubbling singularities along a 2D heat flow with exponential nonlinearity

Frédéric Robert
Institut Élie Cartan, Nancy
22 Nov 2010, 3-4pm, Carslaw Room 352

Abstract

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

${e}^{{u}^{2}}{\partial }_{t}u-{\Delta }_{x}u=\lambda \left(t\right)u{e}^{{u}^{2}},$

where $u:\left[0,\infty \right)×\Omega \to ℝ$ 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.)