Convergence and metastability of (weakly) nonconvex gradient flows

Abstract: Together with Felix Otto, Richard Schubert, and other collaborators, we have developed two different energy-based methods to capture convergence and metastability. We have used these methods to establish optimal, algebraic convergence for the Mullins-Sekerka (MS) problem in the plane and the Cahn-Hilliard equation on the line. After a general introduction of the central ideas, we comment in particular on the role of curvature in the MS problem. Work in progress with Richard Schubert and Felix Otto extends the L1-based method to the Mullins-Sekerka evolution in three dimensions.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php