MA8105 Nonlinear Partial Differential Equations and Sobolev Spaces
General information
Lecturer:
Lectures:
- Tuesday ….. 08:15-10:00 … room 656 (Sima-stuen, SB2)
- Thursday … 14:15-16:00 … room 734 (SB2)
- Plan/log, see 'Lectures' in the left menu.
Exercises:
- Weekly exercises.
- Hints, partial solutions, or references in Appendix C in the lecture note.
Lecture note
- Holden: Tools from the toolbox. Functional Analysis for Partial Differential Equations.
- You will get the note at the first lecture.
Other relevant books
Not part of the curriculum.
- Brezis: Functional Analysis, Sobolev Spaces, and Partial Differential Equations, Springer 2011. (Chapters 1, 3, 4, 8, 9 are relevant)
- Ciarlet: Linear and Nonlinear Functional Analaysis with Applications, SIAM 2013.
- Evans: Partial Differential Equations, AMS 2010. (Chapter 5 on Sobolev spaces)
- Gilbarg and Trudinger: Elliptic Partial Differential Equations of Second Order, Springer 1998. (Chapter 7 on Sobolev spaces)
- Holden, Risebro: Front Tracking for Hyperbolic Conservation Laws, Springer 2015. (Appendix A on compactness, chapter 3 on finite difference methods)
Final Curriculum
- From Holden Tools from the toolbox: sections 1, 2.1, 3, 4.1-4.5, 4.7, 5.1-5.5, 5.7, 7 (Theorem 7.1 with proof), Appendix A (except Theorem A2 and A3), Appendix B.
- Handwritten notes by Espen on Finite difference approximation of Porous Medium Equations.
- All homework problems.
Office hours
Date | Time | Room |
---|---|---|
02.05. | 10:00-11:00 | 1148, SB2 |
09.05. | 10:00-11:00 | 1148, SB2 |
12.05. | 14:00-15:30 | 1148, SB2 |
16.05. | 14:00-15:30 | 1148, SB2 (734 if many come) |
19.05. | 14:00-15:00 | 1148, SB2 |
20.05. – 28.05. | unavailable |
Exam
- Oral
- 2 exam dates: 16.05. and 29.05.
- The exam has two parts:
- (20 min): One of the topics given below is randomly selected and the candidate then gives a presentation of it on the blackboard (no slides).
Focus on the main parts of the topic, or if the topic is big, a selected part of it. Proofs are encouraged.
Notes are allowed - but watch the time - 20 min.
- (25 min): Examination in all of the curriculum. No notes.
- Topics (from Tools from the toolbox): (A) Sections 2.1; (B) Chapter 3; (C) Sections 4.1-4.3; (D) Sections 4.4-4.5, 4.7; (E) Sections 5.1-5.3; (F) Sections 5.4-5.6, 5.7.
- Schedule:
Date | Time | Room |
---|---|---|
16.05. | 09:15 - 10:00 | 734 |
10:00 - 10:45 | 734 | |
29.05. | 09:00 - 09:45 | 734 |
09:45 - 10:30 | 734 | |
10:45 - 11:30 | 734 | |
11:30 - 12:15 | 734 | |
13:15 - 14:00 | 822 | |
26.06. | 08:30 - 09:15 | 734 |