Nonlinear Diffusion Problems, fall 2014
Basic knowledge of linear algebra, ordinary differential equations (in particular phase plane analysis) and linear partial differential
equations. A tiny bit of functional analysis.
The course is concerned with spatio-temporal patterns and has multiple aims :
- provide biological motivation, explain modelling approaches, interpret mathematical results in order to obtain biological insights
- treat nonlinear diffusion problems as examples of infinite dimensional dynamical systems (discuss stability and bifurcation)
- introduce the maximum principle as a fundamental tool for scalar equations
Topics include : travelling waves, asymptotic speed of propagation, Turing patterns, gradient flows
Weeks 44-50, Tuesday 10-12 in room B322 and Thursday 12-14 in room B321. Two hours of exercise classes per week.
by way of projects, taking the results of Exercise elaborations into account; one of the following papers can be used as a basis :
but feel free to come up with your own suggestion. In any case, please contact the lecturer in order to get to an agreement.
Chapters 1-3 (see lecture1.pdf for a shorter version)
syllabus_ch4.pdf (also see lecture2.pdf)
syllabus_ch5.pdf (also see lecture3:4.pdf)
syllabus_ch6.pdf (also see lecture5:6.pdf)
chapter VII of nonlinearanalysis2.pdf from the Bibliography
chapters II , III , V from nonlineardiffusioncwisyllabus.pdf
chapter IV from nonlineardiffusioncwisyllabus.pdf
Did you forget to register? What to do?
October 31 : the two exercises from page 2.2 and the two from page 2.3 of Chapters 1-3
Section 4.4 of syllabus_ch4
November 7 : Section 5.3 of syllabus_ch5 Solutions 1
November 21 : choice of paper for project, discussion about project
November 28 : the exercises from pages 20, 21, 22 and 26 of lecture7:8.pdf Solutions 3
December 5 : the exercises from pages 30 and 31 of lecture9:10.pdf Solutions 4
Update! Downdate!! Because of this thing called Christmas: There is an Exercise class (It had been removed to the last week); exercises 6.6.14 - 6.6.17 of syllabus_ch6. Solutions 5
December 19 : Prepare your Project (And Have a Merry Christmas)