Gradient flow techniques in Partial Differential Equations

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)

Date and time info
Tuesday, 09.00 - 11.00 (will start on November, 5th)

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

Language
English