Teaching / Course archive
Math 581: Winter 2019
PDE 2
Course Record
Overview
PDE II course connecting heat and wave equations with distributions, Fourier methods, hypoellipticity, well-posedness, semilinear problems, and Navier-Stokes equations.
Schedule and Topics
| Date | Topic |
|---|---|
| T 1/8 | Green's identities for the heat operator and the Euclidean heat kernel. |
| T 1/22 | Spectral resolution of the heat equation, smoothing, decay, and backward ill-posedness. |
| R 1/31 | Distributions. |
| R 2/7 | Fourier transform and tempered distributions. |
| T 2/12 | Cauchy problem for wave equations. |
| R 2/21 | Morawetz estimate on local energy decay. |
| T 2/26 | Cauchy-Kovalevskaya theorem. |
| R 3/21 | Malgrange-Ehrenpreis theorem and Hormander's theorem on hypoellipticity. |
| T 4/9 | Duhamel's principle and semilinear problems. |
| R 4/11 | Sobolev algebras, Ladyzhenskaya inequality, and Navier-Stokes equations. |
Topic List
- Heat and wave equations
- Tempered distributions, convolution, and Fourier transform
- Fourier analytic treatment of Sobolev spaces
- Half-space problems and elliptic, parabolic, and hyperbolic behavior
- Semilinear evolution equations
- Navier-Stokes equations and related turbulence models
Books and Related Pages
Books
- Lawrence C. Evans, Partial differential equations. AMS, 1998.
- Fritz John, Partial differential equations. Springer, 1982.
Assignments and Projects
Assignments and Exams
- Assignments 1-5.
- Course project.
Projects
- Thomas Tendron: Kolmogorov-Petrowsky-Piskunov equations
Archive Note
Only project items represented by localized files are linked below.