Seminar Partielle Differentialgleichungen WS2015/16

Vortragsthemen

  • Das Mullins-Sekerka Problem als Gradientenfluss. Formulierung von Mullins-Sekerka als freies Randwertproblem, Einführung des $H^{-1}$-Skalarprodukts und Interpretation von MS als Gradientenfluss. [Pego05],[DaPe05],[Dai05] p.45-62
  • Motion by Mean Curvature as the Singular Limit of Ginzburg-Landau Dynamics. [BrKo91]
  • Variational Models for Phase Transitions, an Approach via Gamma-Convergence. [Albe98]
  • Some aspects of the variational nature of mean curvature flow. [BeMu08] Abschnitt 2 zur Wärmeleitungsgleichung. Verbindung zur Theorie großer Abweichungen.
  • On an Isoperimetric Problem with a Competing Nonlocal Term I: The Planar Case. [KnMu12]
  • Singular perturbations as a selection criterion for periodic minimizing sequences. [Muel93]
  • Mountain pass Theorem. Existenz kritischer Punkte von Funktionalen. [Evan10] p.501
  • Kohn-Otto Technik für Vergröberungsraten, und Anwendungen. _[Pego05] Sec. 4.1 -4.3
  • Weitere Themen auf Anfrage.

Termine

  • 29. September: Stephan Hausberg, Nils Dabrock, Keith Anguige, Carsten Zwilling
  • 28. Januar: Tim Czerwonka, Till Koch, Sebastian Sewarte

Literatur

  • [[Albe98]] Alberti, G., Variational Models for Phase Transitions, an Approach via Gamma-Convergence., (1998)
  • [AtBM14] Attouch, H., Buttazzo, G. and Michaille, Gé., Variational analysis in Sobolev and BV spaces,(2014).
  • [BrKo91] Bronsard, L., Kohn, R., Motion by Mean Curvature as the Singular Limit of Ginzburg-Landau Dynanamics., Journal of Differential Equations 90, 211-237 (1991).
  • [[Dai05]] Dai, S., Universal bounds on coarsening rates for some models of phase transitions. PhD thesis.
  • [DaPe05] Dai, S. and Pego, R., Universal Bounds on Coarsening Rates for Mean-Field Models of Phase Transitions, SIAM Journal on Mathematical Analysis 37 (2) pp. 347-371, (2005).
  • [Evan10] Evans, L. C., Partial differential equations, Providence, RI, (1998).
  • [KnMu13] Knüpfer, H. & Muratov, C. B., On an Isoperimetric Problem with a Competing Nonlocal Term I: The Planar Case, Communications on Pure and Applied Mathematics, Wiley Online Library, (2013).
  • [Muel93] Müller, S., Singular perturbations as a selection criterion for periodic minimizing sequences, Calc. Var. PDE 1, 169-204 (1993)
  • [[Pego05]] Pego, B., Lectures on dynamics in models of coarsening and coagulation.