Instructor. Sigurd Angenent, van vleck hall 609. (2018)
Prerequisites. This course is a sequel to math 819, graduate PDE. However, any student with an interest in PDE and a background in analysis (math 721, and some familiarity with Sobolev spaces) should be able to follow the course.
Topics. The first third of the semester will cover Linear Evolution Equations, following chapter 7 from Evans’ textbook. Following that, we will study a number of examples of nonlinear evolution equations, in particular
- Two parabolic equations: The Allen Cahn equation; The porous medium equation; Mean curvature flow.
- The Navier Stokes equation.
- Hyperbolic equations and conservation laws.
- A brief introduction to dispersive equations (time permitting).
Homework. There will be short homework assignments every other week.
Textbook. L.C.Evans, Partial Differential Equations, 2nd edition, AMS monographs. Book website