Vivi Rottschäfer (kamer 206), Jens Rademacher (202 only Monday)

Assistant: Frits Veerman (202)

Literature

**Main textbook:**P. Grindrod, The theory and applications of reaction-diffusion equations - Patterns and waves, 2nd edition Clarendron Press 1996- B. Sandstede, Stability of travelling waves. In: Handbook of dynamical systems II.(B Fiedler, ed.). North-Holland (2002) 983-1055
- Dan Henry. Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics 840. Springer 1980.
- R. Hoyle, Pattern formation - an introduction to methods. Cambridge 2006
- L. Pismen, Patterns and interfaces in dissipative dynamics. Springer 2006
- R. Kapral, K. Showalter, Chemical waves and patterns. Kluwer 1994

- Software applications on DSWeb
- Simple Matlab scripts for simulation of the bistable example (update)
- Links to pictures and movies

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

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) |