Teaching / Course archive
Math 581: Winter 2021
PDE 2
Course Record
Overview
PDE II course focused on nonlinear problems, with Sobolev spaces, Fourier transform, and functional analytic methods used throughout.
Schedule and Topics
Topic List
- Cauchy-Kovalevskaya theorem, Holmgren's theorem, and characteristic surfaces
- Distributions, convolution, Fourier transform, and fundamental solutions
- Constant coefficient operators, hypoellipticity, and the Malgrange-Ehrenpreis theorem
- Ellipticity, parabolicity, hyperbolicity, and well-posedness
- Sobolev spaces, semilinear evolution equations, and applications to Navier-Stokes type problems
Books and Related Pages
Books
- Gerald B. Folland, Introduction to partial differential equations. Princeton, 1995.
Related Course Pages
Assignments and Projects
Assignments and Exams
- Homework assignments and a course project.
Archive Note
The recovered page contains the outline but no detailed public schedule.