Course Objectives: The course covers mathematical analysis of applied nonlinear partial differential equations. The material focuses on well-posedness of hyperbolic, elliptic, and parabolic 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.
Topics: quasi-linear first-order systems of 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, HH-422, ext.23424, e-mail: email@example.com
Lectures: Monday (10:30-12:00), Thursday (9:30-11:00); HH/207
Office hours: Tuesday, Thursday (9:30-11:30), or by appointment
"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)
Assignments: Four home assignments will be handed out in class on Mondays every third week, starting the week of January 12. The assignments are due 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.
Project - 40%
Assignments - 60%