Winter 2012/13

Differential Equations II

PD Dr. Pavel Gurevich

Recitation session: Dr Sergey Tikhomirov

Schedule, Winter 2012/13

Lecture:

Tuesday 10.15-12.00, Arnimallee 6 SR 025/026

Thursday 10.15-12:00, Arnimallee 6 SR 025/026

Recitation session:

Friday, 10.15-12.00, Arnimallee 7 R 140

Topics

This course will mainly deal with linear partial differential equations (PDE). The contents is as follows:

1. First order nonlinear PDE. Characteristics.
2. Motivating examples leading to PDE. Setting of problems.
3. Classification of second-order PDE: elliptic, parabolic, and hyperbolic equations
4. Functional spaces: Lebesgue and Sobolev spaces
5. Elliptic PDE. Spectral theory of elliptic PDE. Regularity of solutions.
6. Hyperbolic PDE. Classical solutions. Initial boundary-value problems. Fourier method.
7. Parabolic PDE. Classical solutions. Initial boundary-value problems. Fourier method.

Literature

1. L.C. Evans. Partial Differential Equations. Second edition. Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 2010.
2. V.P. Mikhailov. Partial Differential Equations. Translated from the Russian. ``Mir'', Moscow; distributed by Imported Publications, Inc., Chicago, Ill., 1978.
3. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Appl. Math. Sci., vol. 44, Springer, New York, 1983.
4. D. Henry. Geometric theory of semilinear parabolic equations. Lecture Notes in Mathematics, vol. 840, Springer, Berlin-New York, 1981.

Homework assignments, Winter 2012/13

1. First assignment, due Wednesday, October 24, 2012, at 12:00 (PDF)
2. Second assignment, due Wednesday, October 31, 2012, at 14:00 (PDF)
3. Third assignment, due Wednesday, November 7, 2012, at 14:00 (PDF)
4. Forth assignment, due Wednesday, November 14, 2012, at 14:00 (PDF)
5. Fifth assignment, due Wednesday, November 21, 2012, at 14:00 (PDF)
6. Sixth assignment, due Tuesday-Wednesday, November 27-28, 2012, at 14:00 (PDF)
7. Seventh assignment, due Tuesday, December 4, 2012, at 16:00 (PDF)
8. Eight assignment, due Tuesday, December 11, 2012, at 16:00 (PDF)
9. Ninth assignment, due Tuesday, December 18, 2012, at 16:00 (PDF)
10. Ten's assignment, due Tuesday, January 8, 2013, at 16:00 (PDF)
11. Merry Christmas!
12. Eleventh assignment, due Tuesday, January 15, 2013, at 16:00 (PDF)
13. Twelfth assignment, due Tuesday, January 22, 2013, at 16:00 (PDF)
14. Thirteenth assignment, due Tuesday, January 29, 2013, at 16:00 (PDF)
15. !Updated! Fourteenth assignment due Thursday, February 7, 2013, at 12:00 (PDF)

Please use the appropriate boxes, Arnimallee 3, upstairs.

Exam

1. The exam will take place February 15, 10:00. Raum: Hs B Horsaal/Arnim 22.
2. Questions
3. First examination problems (PDF)
4. First examination results
5. The second exam will take place April 15, 12:00-14:00. Takustr. 9, Seminarraum 049.
6. Second examination results