Graduate

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. (chap. 2.3)
Sep 4 – 6 Labor day – Laplace eq. (chap. 2.2)
Sep 11 – 13 Laplace eq. (chap. 2.2) – Functional analysis (chap. 5.2)
Sep 18 – 20 Functional analysis (chap. 5.2)
(supplement weak convergence)
Sep 25 – 27 Approximation – Trace (chap. 5.3, 5.5)
Oct 2 – 4 Compact embedding (chap. 5.7), Elliptic eq. (chap. 6.1)
Oct 9 – 11 Fall Break
Oct 18 – 20 Weak solution – Lax-Milgram (chap. 6.1-6.2)
Oct 23 – 25 Eigenvalues-regularity (chap. 6.3-6.5)
Oct 30 – Nov 1 Linear evolution eq. (chap. 7.1)
Nov 13 – Nov 15 Linear evolution eq. (chap. 7.1)

Class homework

Sep 6 HW1 (solution, TeX)
Sep 27 HW2 (solution)
Oct 23 HW3 (solution)
Nov 13 HW4