U Leiden, Spring 2010: Introduction to pattern formation

1 Feb to 17 May 2010, Mondays 11.15-13h (not 22. March, 5. April, 3. May)
Vivi Rottschäfer (kamer 206), Jens Rademacher (202 only Monday)
Assistant: Frits Veerman (202)



Literature
Resources Homework
  1. Set 1. Strict due date March 1st, 13.45h (Excercise 1 corrected 22. Feb).
  2. Set 2. Strict due date March 29th, 11.15h.
  3. Set 3. New Strict due date April 26th, 11.15h.
  4. Set 4. Strict due date May 25th, 11.15h.
Lecture schedule

    1.2.Introduction
    8.2.The bistable example (Section 1.3, 1.4 until page 24) (Jens)
    15.2.Asymptotics for periodic solutions (Section 1.4 until page 26) (Vivi)
    22.2.Stability and spectra (rest of Section 1.4, see also Scholarpedia, Wikipedia on stability) (Jens)
    1.3.Continuation of previous lecture.
    8.3.Existence of travelling waves (Section 1.5) (Vivi)
    15.3.Local existence theory (Section 1.6, also Henry's book Chapter 3)
    29.3.Blow-up (Vivi)
    12.4.Bifurcations and pattern formation (Section 2) (Jens)
    19.4.Boundary layers (Section 2.2) (Vivi)
    26.4.Turing bifurcation, concepts of centre manifolds (Section 2.1) (Jens)
    10.5.Oscillatory instability: Andronov-Hopf bifurcation (Section 2.3 (?) ) (Vivi)
    17.5.Lyapunov-Schmidt reduction (Box H) and wrap-up (Jens)