Partial Differential Equations II

(Fall, 2002)

**Course Objectives:**
The course covers advanced aspects of mathematical analysis
of partial differential equations. The material focuses on
well-posedness of elliptic, parabolic, and hyperbolic equations,
which includes existence, uniqueness and stability of solutions.
Lectures contain both results and derivations.
All assignments are home-taken and based on a number of
analytical problems. The course follows the preliminary set-up
of the pre-requisited course Math3FF3 (PDE I) and extends the material
to the fourth-year (Math4GG3) and graduate (Math742) students.

**Topics:**
quasi-linear first-order equations;
elliptic, parabolic, and hyperbolic second-order equations;
applied nonlinear equations in one, two and three space dimensions,
methods of analysis: characteristics, Riemann invariants,
spectral transforms, variational and maximum principle,
Green's functions, Riemann-Hilbert problems, inverse scattering
transform.

**Instructor:**
Dr. Dmitry Pelinovsky, BSB-204, ext.23424,
e-mail: dmpeli@math.mcmaster.ca

**Hours:**

*Lectures:* Monday, Wednesday, Thursday (13:30-14:20); KTH/107

*Office hours:* Tuesday (9:30-10:20),
Thursday (14:30-15:20), or by appointment

**Textbooks:**

*"Applied Partial Differential Equations"*
by J. Ockendon, S. Howison, A. Lacey, and A. Movchan (Oxford University Press, 1999)

*"Partial Differential Equations"*
by F. John (Springer-Verlag, 1998)

**Course webpage:** http://dmpeli.math.mcmaster.ca/ (Partial Diff Eqs II)

**Assignments:**
Four home assignments will be handed out in class on Mondays every third
week, starting the week of September 16. The assignments are due
at 14:20 on Thursdays in the following week. The texts for assignments
and solutions will be posted on the course webpage.

**Project:** The course is completed by a take-home project.
Details of the project will be announced in mid-term.

**Marking scheme:**

Project - 40% Assignments - 60% |