Musterbildung, Energielandschaften und Skalierungsgesetze

Direktor:
Felix Otto

Kontakt: Email
Telefon:
+49 (0) 341 - 9959 - 950
Fax:
+49 (0) 341 - 9959 - 585

Anschrift:
Inselstr. 22
04103 Leipzig

Sekretariat:
Katja Heid
Email
, Telefon:
+49 (0) 341 - 9959 - 951

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

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)
15.10.2019, 14:52