AM 224 SYLLABUS, Spring 2006
AM 223-224 (MA 237-238) is the core graduate sequence on partial differential
equations. In the first semester, the focus was
on the basic theory of linear equations. This semester, we will
mainly study nonlinear equations. The plan is
to cover as much is possible of the following topics:
- Scalar conservation laws and Hamilton-Jacobi equations.
- Sobolev inequalities and Sobolev spaces.
- The direct method in the calculus of variations.
- Elliptic regularity.
- Symmetric hyperbolic systems.
Prerequisites: Real analysis (AM 211, MA 221 or equivalent) and AM 223
(MA 237).
Textbooks: The two main sources for the class this semester will be
- L. C. Evans, Partial differential equations , AMS 1998.
- L. C. Evans, Weak convergence methods for nonlinear
PDE , AMS, 1988.
As in AM 223, a few representative examples will be treated in depth,
and this will often mean consulting other sources, including original
papers. To the extent possible, I will try to hand out notes.
The following sources will be useful at different points:
- C.M. Dafermos, Hyperbolic conservation laws in
continuum physics , Springer, 200.
- F. John, Partial differential equations , Springer 1981.
- D. Gilbarg and N. Trudinger, Elliptic partial differential
equations of second order , Springer 2001.
- M. Struwe, Variational methods ,
Springer, 2000.
Lecture Notes
Here is a transcript of the lectures by
Andreas Kloeckner.
Here is Andreas' English translation of Hopf's
paper on the Navier-Stokes equations.
Homework
HW 1 , Solutions .
HW 2 , Solutions .
HW 3 , Solutions .
HW 4 , Solutions .
HW 5 , Solutions .
HW 6 , Solutions .
Exam .
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On 24 Jan 2006, 16:47.