**Instructor. ** Sigurd Angenent, van vleck hall 609.

**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 Evansâ€™ 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