MA8105 Nonlinear Partial Differential Equations and Sobolev Spaces
- Monday 14:15-16:00 in B23 (Berg)
- Friday 10:15-12:00 in S21 (SB2)
- Plan/log, see 'Lectures' in the left menu.
- Weekly exercises, see "Execises" in the left menu.
- Hints, partial solutions, or references in Appendix C in the lecture note.
- Problem session: Friday 9:15-10:00, room 656 SB2 (student run)
- 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)
- Vazquez: The Porous Medium Equation, Oxford 2007.
- Folland: Real Analysis, Wiley 1999. (Chapter 7 on Radon measures)
- 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 Porous Medium Equations.
- All homework problems.
- 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.
|15.05.||Wednesday||09:25-10:10||Room 1148, SB2||Helge|
|10:15-11:00||Room 1148, SB2||Max|
|27.05.||Monday||13:15-13:00||Room 1148, SB2||Erik|
|14:05-14:50||Room 1148, SB2||Ola|
|29.05.||Wednesday||14:15-15:00||Room 1148, SB2||Ling|
|15:05-15:50||Room 1148, SB2||Morten|
|15:55-16:40||Room 1148, SB2||Olav|