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Nonlinear Diffusion Problems, fall 2014

Lecturer

Odo Diekmann

Scope

6 sp.

Type

Advanced studies

Prerequisites   

Basic knowledge of linear algebra, ordinary differential equations (in particular phase plane analysis) and linear partial differential
equations. A tiny bit of functional analysis.

Content

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

 

Lectures

Weeks 44-50, Tuesday 10-12 in room B322 and Thursday 12-14 in room B321. Two hours of exercise classes per week.

lecture1.pdf

lecture2.pdf

lecture3:4.pdf

lecture5:6.pdf

lecture7:8.pdf

Erratumpage722.pdf

lecture9:10.pdf

lecture11.pdf

lecture12.pdf

lecture13.pdf

lecture14.pdf

Exam

by way of projects, taking the results of Exercise elaborations into account; one of the following papers can be used as a basis :

driftparadox.pdf

climate.pdf

louintro.pdf

othmerstevens.pdf

hillenpainter.pdf

du-matano.pdf

angenent.pdf

dancer.pdf

but feel free to come up with your own suggestion. In any case, please contact the lecturer in order to get to an agreement.

Lecture notes

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

syllabus_ch7.pdf

Bibliography

nonlineardiffusioncwisyllabus.pdf

nonlinearanalysis1.pdf

nonlinearanalysis2.pdf

amsbookreview.pdf

LNinBiomath68.pdf

 

Registration

 
Did you forget to register?  What to do?

Exercises

GroupDayTimePlaceTeacher
1.Friday12-14B322Anssi Mirka

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 14 :  14novexercises.pdf                   Solutions 2

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

December 12: 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)                          

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