Graduate

APM 577: Theory of PDE II

Spring 2018

Class Time Tu,Th 9:00 – 10:15
Class Location Tempe – Discvry 350
Instructor S├ębastien 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 Fixed point methods (chap. 9.2)
Mar 27 – Mar 29 Fixed point methods (chap. 9.2)
Apr 3 – Apr 5 Super-sub solutions (chap. 9.3)

Class homework

Jan 29 HW1
March 27 HW2