Mathematics 727: Partial Differential Operators (Fall, 2022)

Course Information

Course Objectives: The course covers selected chapters in the analysis of linear and nonlinear partial differential equations. Topics include properties of Fourier transform in Lebesgue spaces, well-posedness (existence, uniqueness, and continuous dependence) of partial differential equations in Sobolev spaces, stability of nonlinear waves in Hamiltonian systems.

Instructor: Dr. Dmitry Pelinovsky, HH-422, ext.23424, e-mail:

Lectures: Wednesday, Thursday (11:00-12:30); HH-207
Office hours: Wednesday (10:00-11:00,12:30-1:30), or by appointment

E. Lieb and M. Loss, "Analysis" (Graduate Studies in Mathematics, Volume 14, AMS, 2001)
F. Linares, G. Ponce, "Introduction to Nonlinear Dispersive Equations" (Springer, Universitext), 2009, ISBN 9780387848983
A. Geyer, D. E. Pelinovsky ``Stability of nonlinear waves in Hamiltonian dynamical systems" (preprint)

Assignments: Three home assignments will be posted on the course webpage with some specific assignments.

Final exam: The course is completed with student presentations. Details of the presentations will be announced in November.

Marking scheme:
Class participation - 30%
Final presentation - 40%
Three assignments - 30%