Fall 2024, Math 251A

Introduction to PDEs

Time/Place: MWF at 10am in MS 5118

Office hours: Mondays 12-1, Fridays 2-3 at MS 7923

Textbooks: (Main) Evans, Partial Differential Equations,

J. Jost, PDEs.

Topics to be discussed:

1. Basic linear PDEs and their properties: Chapter 2 of Evans.

2. Hamilton-Jacobi equation and Conservation law: Chapter 3 of Evans.

3. Elliptic and Parabolic equations: maximum principle, existence, uniqueness, stability: Evans and Jost.

4. Viscous Hamilton-Jacobi equation and Optimal control theory: Chapter 10 of Evans.

5. (If time permits) Lagrangian flows: The main reference is the following paper:

The course requires some exposure to basic measure theory. We will also go through some material from measure theory as needed in the class.

Grading is based on the completion of 5-6 homework assignments. Homework will be assigned on Thursdays and will be due the Wednesday after.

Homework problems

Homework 1: Here. (Due 10/16)

Homework 3: Here (Due 11/15)