# MA8105 Nonlinear Partial Differential Equations and Sobolev Spaces

# General information

### Lecturer:

### Lectures:

- Monday 14:15-16:00 in B23 (Berg)

- Friday 10:15-12:00 in S21 (SB2)

- Plan/log, see 'Lectures' in the left menu.

### Exercises:

- 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)

### 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)

- Vazquez:
*The Porous Medium Equation*, Oxford 2007.

- Folland:
*Real Analysis*, Wiley 1999. (Chapter 7 on Radon measures)

### 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 Porous Medium Equations.

- All homework problems.

### Exam

- Oral

- 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.

- Dates:

Date | Day | Time | Room | Candidate |
---|---|---|---|---|

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 |