PDE Seminar Abstracts

Let $\Omega \subset {\mathbb{R}}^{2}$ 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 $u:\left[0,\infty \right)\times \Omega \to \mathbb{R}$ 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.)

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