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:
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Project - 40% Assignments - 60% |