Pattern formation, energy landscapes, and scaling laws

Felix Otto

Contact: Email
+49 (0) 341 - 9959 - 950

Inselstr. 22
04103 Leipzig

Administrative Assistant:
Katja Heid
Email, Phone/Fax:
+49 (0) 341 - 9959
- 951
- 658

Lectures in the Winter term 2013 / 2014

Gradient flow techniques in Partial Differential Equations

  • 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


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)
20.03.2023, 09:09