Reaction diffusion equations - Cambridge, Michaelmas 2011

  • This information is also available at the APDE Teaching homepage .
  • Recommended literature:
    1. L. C. Evans, Partial Differential Equations, AMS
    2. P. Grindrod, Patterns and Waves: The Theory and Applications of Reaction-Diffusion Equations, Clarendon Press
    3. J.D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, Springer
    4. K. Fellner, Lecture notes on "Reaction diffusion equations", Cambridge, Michaelmas 2010
    5. B. Perthame, Lecture notes on "Growth, reaction, movement and diffusion from biology"

  • Example Sheets: Examples 1 , Examples 2 , Examples 3

  • Matlab source codes: for the last two examples you need the function laplacian
    1. Predator and prey ; Turing instabilities in a simple 1D predator and prey model
    2. Fisher/KPP equation ; Travelling wave solutions of the Fisher/KPP equation
    3. Chaffee-Infante problem ; Approximate solution of the Chaffee-Infante problem
    4. Diffusive version of Fitz-Hugh-Nagumo system ; Travelling pulse solutions in 1D
    5. Nonlocal Fisher/KPP equation ; Turing instabilities in 2D
    6. Schnakenberg system ; Pattern formation in 2D