Partial Differential Equations, 5 credit points

Graduate Course, period 3-4, 2005-06

Teacher: Stig Larsson

Literature: L. C. Evans, Partial Differential Equations,
Graduate Studies in Mathematics 19, American Mathematical Society, 1998.
It can also be ordered from, for example, Bokus or Adlibris.

The purpose of the course is to introduce the student to the state of the art of the modern theory of partial differential equations.
We will study chapters 1-7 (with some omissions), and some selected topics from chapters 8-11.

Examination: To pass the course you need x points earned on the following activities:

• each good solution of a homework problem gives 1 point;
• written theory exam, max 10 points;
• student lecture, 5 points (more details will be given later).

More details will follow here later on.

Check your points here.

Schedule: (with exceptions indicated in the plan below)

Lectures: Tuesday 13.15-15, room MV:L15

Exercises: Thursday 8.15-10, room MV:L14

Plan of the teaching: (to be completed as we go along)

week 6 Feb 6-12

Introductory meeting: Thursday February 9, 11.00, in my office MV:L2078.

week 7 Feb 13-19

Read: Ch 1, 2.1, 2.2. Take a quick look at Appendices A - E.

Lecture: Ch 2.2 (Thursday 16/2 8.15-10, room MV:L14)

week 8 Feb 20-26

Read:

Lecture: Ch 2.2 continued. (Tuesday 21/2 13-15, room MV:F32)

Exercises: 1.3, 1.4, 2.2, 2.3. [We did: 1.3 (Aron), 1.4 (Fardin), 2.2 (Mikael), 2.3 (Stig)] Hand in: 2.4 (Thursday 23/2 8.15-10, room MV:L14)

week 9 Feb 27-Mar 5

No teaching. [ Going to the Univ of Florida, Tallahassee, :-) ]

Read: Ch 2.3

Exercises:

week 10

Read: Ch 2.3, 2.4.

Tuesday March 7. Lecture cancelled.

Thursday March 9. Lecture: Ch 2.3.

week 11

Tuesday March 14. Lecture: Ch 2.4 (2.4.1 a,b,c n=3 with proofs, the rest without proofs, 2.4.2 without proofs, 2.4.3 with proofs.)

Thursday March 16. Exercises, we did: 2.5 (Fardin), 2.6 (Aron), 2.7 (Fardin), 2.8 (Marcus). Hand in: 2.13, 2.16

week 12

Tuesday lecture: 3.1, 3.2.

Thursday exercises, we did: 2.9 (Mikael), 3.2 (Aron), 3.3a (Aron).

week 13

Skip 3.4. Read 3.4, Theorems 1,2,3 without proof, Theorem 4 with proof. Skip 3.4.5.

Tuesday lecture: 3.4, 5.1, 5.2

Thursday exercises: we did 3.13 (Mikael), 5.1 (Fardin), 5.2 (Aron), 5.4 (Mikael). Hand in: 5.3.

week 14

Read ch 5.

Tuesday lecture: 5.3, 5.4, 5.6

Thursday lecture: 5.6-5.7

week 15

No teaching this week.

week 16

Tuesday lecture: 6.1, 6.2

Thursday exercises: we did 5.5 (Aron), 5.6 (Fardin), 5.7, 5.8 (Fredrik), 5.9. Hand in: 5.10

week 17

Tuesday lecture: 6.3

Thursday exercises: hand in: 5.17

week 18

Tuesday lecture: 6.4

Exercises, we did: 5.11, 5.12 (Mikael), 6.1 (Fredrik)

week 19

Tuesday lecture: 6.5

Exercises, we did: 6.4, 6.6, 6.7, 6.8

week 20

Student lecture, Monday 8.30-10: Semigroups (Mikael).

Tuesday lecture: Semigroups, continued (Mikael). 7.1

Exercises:

week 21

Tuesday lecture: 7.1

Thursday: holiday.

week 22 May 29-June 3

Tuesday lecture: 7.1 (skip proofs of Harnack and strong max principle)

Thursday lecture: 7.2

week 23

Thursday June 8, 9-10, student lecture: Fredrik, 4.3 Transform methods

Thursday June 8, 10-11, student lecture: Aron, Sobolev spaces based on F-transform

Thursday June 8, 11-12, student lecture: Fardin, 3.3 Hamilton-Jacobi

Thursday June 8, 13-15, student lecture: Marcus, 7.3 First order hyperbolic systems

Friday June 9, 8-10, oral exams Mikael, Aron

Introductory meeting: Thursday February 9, 11.00, in my office MV:L2078.

Welcome!

/stig