##
MTH 627: Advanced Partial Differential Equations (Fall 2017)

**Office Hours:** TBD

We develop the notions of weak derivatives, Sobolev spaces, boundary
trace and weak formulations of elliptic boundary-value problems and of
initial-boundary-value problems for parabolic or hyperbolic
PDEs. These are resolved by variants of the closed-range theorem,
variational methods, and the generation theory of semigroups of
contractions. Extensions to nonlinear problems and systems will be
presented (as Supplementry material) according to the interests of the
class.

**Prerequisite: ** MTH 622 or MTH 513 or consent of instructor.

Questions to the instructor about prerequisites and expectations
are welcome.

**Textbook : ** Hilbert Space Methods for PDEs. It is also available
from **Dover**.

Supplementary notes.pdf will be available.

**Grades ** are based on problem sets (Homework) and
progress relative to previous experience.

**Schedule:**

1. HSM Chapter 1:
pp. 1 - 18.

2. HSM Chapter 2:
pp. 31 - 35, generalized functions.