## APM 577: Theory of PDE II

## Spring 2018

Class Time |
Tu,Th 9:00 – 10:15 |

Class Location |
Tempe – Discvry 350 |

Instructor |
Sébastien Motsch |

Office |
WXLRA 836 |

Email |
smotsch@asu[dot]edu |

Office Hours |
Tu,Th 10:30am – 11:30am |

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

## Textbook

- L. Evans,
* Partial Differential Equations * (2nd edition)

### 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) Non-linear 1st order PDEs
*(Chap. 3.1-3.3)*
- b) Variational method for non-linear PDE
*(Chap. 8)*
- c) Non-variational method
*(Chap. 9)*
- d) Systems of conservation laws
*(Chap. 11)*

### Class Schedule

Jan 9 – 11 |
Complete integrals, envelope (*chap. 3.1*) |

Jan 16 – 18 |
Characteristic eq., Hamilton-Jacobi (*chap. 3.2-3.3*) |

Jan 23 – 25 |
Hamilton-Jacobi (*chap. 3.3*) |

Jan 30 – Feb 1 |
Conservation laws (*chap. 3.4*) |

Feb 6 – 8 |
Conservation laws (*chap. 3.4*) |

Feb 13 – 15 |
Calculus of variations (*chap. 8.1*) |

Feb 20 – 22 |
Conference |

Feb 27 – Mar 1 |
Existence of minimizers (*chap. 8.2*) |

Mar 6 – Mar 8 |
Spring break |

Mar 13 – Mar 15 |
Constraints, Mountain-pass theorem (*chap. 8.4-8.5*) |

Mar 20 – Mar 22 |
Non-variational methods (*chap. 9.1-9.2*) |

### Class homework