## APM 576: Theory of PDE I

## Fall 2017

Class Time |
M,W 10:45 – 12:00 |

Class Location |
Tempe – LL 264 |

Instructor |
Sébastien Motsch |

Office |
WXLRA 836 |

Email |
smotsch@asu[dot]edu |

Office Hours |
M,W 1:00pm – 3:00pm |

Class webpage |
www.seb-motsch.com/graduate |

## Textbook

- L. Evans,
* Partial Differential Equations * (2nd edition)
- Additional: H. Brézis,
* Functional Analysis, Sobolev Spaces and Partial Differential Equations*

### Course description

This course introduces rigorous methods to study partial differential equations such as existence theory and global behavior of solutions. The goal is to understand *intuitively* PDEs and then to develop analytic skills to * prove* results. This class is intended to be spread over two semesters, the first semester will be focused on **linear PDEs** (e.g. elliptic, parabolic equations) and the second semester on **non-linear PDEs** (e.g. conservation laws, Hamilton-Jacobi equations).

The course will be divided in four parts:

- a) Review PDEs
*(Chap. 1, Chap. 2.1-2.3)*
- b) Functional analysis
*(Chap. 5.2-5.7)*
- c) Elliptic PDEs
*(Chap. 6)*
- d) Evolution equations
*(Chap. 7)*

### Class Schedule

Aug 21 – 23 |
Intro. (*chap. 1*), Transport eq. (*chap. 2.1*) |

Aug 28 – 30 |
Heat eq., Laplace eq. (*chap. 2.2-2.3*) |

### Class homework

Sep 4 |
**Chap.2**: to be announced… |