MA8105 Nonlinear Partial Differential Equations and Sobolev Spaces

Spring 2019

Welcome to MA8105 !

  • What is this course about?
    • Mathematical methods and structures that are fundamental for the study of partial differential equations (PDEs), variational calculus, numerical methods etc.
    • Main focus on analytical tools: Functional analysis, \(L^p\) and Sobolov spaces, compactness, modes of convergence, distributions, error estimates.
    • 1-3 weeks on applications to linear and nonlinear PDEs.
  • Who can take this course?
    • Interested students at Master or PhD level.
    • The level should be suitable for good 4th year students in the industrial mathematics program.
    • It can be taken as a regular course or a 'fordypningsemne'.
    • Very relevant for students specialising in PDEs, optimization, analysis, numerical analysis, or probability.
  • Prerequisites:
    • Elementary functional analysis, equivalent to TMA4145 Linear Methods.
    • Some real analysis (Lebesgue integration theory).
    • It is advantageous, but not necessary, to have some background in partial differential equations.

Messages

21.06.2019 Exam August August 15 (Thursday). Room 1148 SB2.

14:15-15:00 TL
15:05-15:50 EHS
15:55-16:40 MGS

Oral exam, same rules as before including 20 min presentation - see "General information" in the left menu.

08.04.2019 Exam dates See "General information" in the left menu

              Office hours See table below

My notes Some of them are posted under "Lectures" in the left menu.

These are the notes for the lectures that deviated substantially from Holden.

I strongly recommend you look at them.

Office hours

Date Time Room
Monday 13.05. 14:15-15:00 Room 1148, SB2 
Friday 24.05. 14:15-16:00 Room 1148, SB2 
Tuesday 28.05. 09:30-11:00 Room 1148, SB2 
05.04.2019 Last lecture Monday April 8

No lecture on Friday April 12

Exam We fix a date or two for the oral exam in the last lecture.

Updated info under "General information".

Reference group We take a last short meeting on Monday.

I need a volunteer to write a (possibly very!) short report on behalf of the students and send it to me.

Final curriculum See "General information" in the left menu.

Info about lectures What did we do + several copies of my lecture notes, see "Lectures" in the left menu.

Solutions Solutions to all exercises available at under "Exercises" in the left menu

03.04.2019 Application The porous medium equation, existence of weak solutions
Convergence of a finite difference approximation
Apriori estimates and compactness.

Exercise 12 and 13 Available at under "Exercises" in the left menu.
Solutions 10 and 11 Available at under "Exercises" in the left menu.
22.03.2019 No lecture on Friday March 29 I am traveling.
Exercise 11 Available at under "Exercises" in the left menu.

Volunteer wanted…
Solutions 8 and 9 Available at under "Exercises" in the left menu.
15.03.2019 3 lectures Week 12 One extra lecture since the week after will only have one lecture (Monday)
Extra lecture Thursday March 21 Room 656 (SIMA stuen) Sentralbygg 2

One of 3 lectures Week 12.

Replaces the Friday lecture in the week after.
Exercise 10 Available at under "Exercises" in the left menu.

Volunteer wanted…
Solutions 7 Available at under "Exercises" in the left menu.
06.03.2019 No lecture Friday March 8 I will be travelling
Exercise 9 Available at under "Exercises" in the left menu.
Solutions 6 Available at under "Exercises" in the left menu.
Voluteers Exercise 8: Alexandra, Exercise 9: Max
25.02.2019 Lecture Thursday March 7 Room 656 sentralbygg 2 (SIMA stuen)

Instead of the lecture Friday March 8  
Exercise 8 Updated! Available at under "Exercises" in the left menu.
Solutions 5 Available at under "Exercises" in the left menu.
20.02.2019 Exercise 7 Available at under "Exercises" in the left menu.

Volunteer wanted…
Solutions 4 Available at under "Exercises" in the left menu.
11.02.2019 No lecture
Monday 18.02.
I will be away that day.
Extra lecture
Thursday 14.02
Auditorium F4 (2nd floor Gamle Fysikk)

To catch up for missing Monday lecture.
Exercise 6 Available at under "Exercises" in the left menu. Volunteer wanted…
Solutions 3 Available at under "Exercises" in the left menu.
Volunteer HW 5 Helge
Reference group = the whole class.

First meeting Monday 11.02. in the break.
Conclusions, see "Reference group" in left menu.
04.02.2019 Alternative lecture time Thursday 14:15-16:00

Some weeks I will travel, then we will use this time.
Exercise 5 Available at under "Exercises" in the left menu.
Solutions 2 Available at under "Exercises" in the left menu.
Voluteers Exercise 3: Morten, Exercise 4: Max
28.01.2019 Exercise 3 and 4 Available at under "Exercises" in the left menu.
Solutions 1 Available at under "Exercises" in the left menu.
19.01.2019 New room Mondays New room: B23, Berg, 4th floor.

Directions can be found here: Maze Map
Monday Jan 21 We meet in room 822 at 14:05,
to go all together to B23.
Exercise 2 Available at under "Exercises" in the left menu.
Problem sessions Fridays 09:15-10:00, room 656 SB2

Student run. One student take special responsibility to look at all problems in advance.

You may ask me for help in the breaks in the lectures or at my office hours.
Office hours Monday 16:15-17:00 room 1148
15.01.2019 Corrections Here is the corrected proof of Proposition 23 in Lecture Monday Jan 14.
Exercise 1 Available at under "Exercises" in the left menu.
Lectures Monday 14:15-16:00, room B23 (Berg, 4th floor)
Friday 10:15-12:00, room S21 (SB2, 2nd floor)
11.01.2019 First Lecture
Lecture note Helge Holden: Tools from the Toolbox. Functional Analysis for PDEs
You will get a free copy on the condition that you do not copy it or pass it on.
12.11.2018 News Lecturer 2019: Espen R. Jakobsen
Curriculum and lecture plan: Similar to 2017, but some changes
Info meeting

Tuesday 08/01/2019

15:15-16:00

room 734, SB2 (7th floor)
If you are interested in this course, you should participate:
- Outline of course.
- Determine lecture times.
- Register for course email list (compulsory).

- Can not attend? Send me an email with your preferred lecture times.

MonTueWedThurFri
08:15 - 09:00     
09:15 - 10:00     
10:15 - 11:00    Lecture
Room S21
11:15 - 12:00    
12:15 - 13:00     
13:15 - 14:00     
14:15 - 15:00Lecture
Room 822 (SB2)
    
15:15 - 16:00    
2019-08-12, Espen Robstad Jakobsen