• Lecturer: Felix Otto
• Date: Tuesday, 09.00 - 11.00 (will start on November, 5th)
• Room: MPI MiS A 01
• Language: English
• Target audience: MSc students, PhD students, Postdocs
• Content (Keywords): PDEs, gradient flow, Stefan Problem, porous medium equation, Cahn-Hilliard equation, Ginzburg-Landau model
• Prerequisites: Analysis, in particular vector calculus, elementary differential geometry, some familiarity with PDEs

Abstract

Many partial differential equations have the structure of a gradient flow on an (infinte-dimensional) Euclidean space or Riemannian manifold. The gradient flow structure encodes the competition between a driving energy and the limiting dissipation (as modeled by the metric tensor). We will show in specific examples how such a gradient flow structure can be used in the analysis of the PDE. Specific examples could include:

• An existence result for a free boundary problem in solidification (Stefan problem) 
• Convergence to a self-similar solution (porous medium equation) 
• Coarsening (Cahn-Hilliard equation)
• Hydrodynamic limits (so-called Ginzburg-Landau model)