Spring Semester 2007

Partial Differential Equations


Quick Links:

This class is an introduction to the theory of partial differential equations. The main topics are: classification of PDEs, linear prototypes (transport equation, Poisson equation, heat equation, wave equation); functional setting, function spaces, variational methods, weak and strong solutions; examples of nonlinear parabolic PDEs, introduction to conservation laws; exact solution techniques, transform methods, power series solutions, asymptotics.

Contact Information:
Instructor:Marcel Oliver
Office hours:  Tu, Th 11:15 in Research I, 107
Grader:Vladimir Molchanov

Time and Place:
Lectures:  Mo 9:45-11:00, We 11:15-12:30 in East Hall 3

Reommended Textbook:
L.C. Evans: Partial Differential Equations


Class Schedule (subject to change!)

05/02/2007: Introduction; linear transport equation
07/02/2007: Laplace equation, fundamental solution
12/02/2007: Poisson equation, mean value formulas
14/02/2007: Harmonic functions: maximum principle, uniqueness for solutions to the Poisson equation, regularity
19/02/2007: Harmonic functions: analyticity
21/02/2007: Harmonic functions: Liouville's theorem, Harnack's inequality
26/02/2007: Dirichlet problem, Green's functions
28/02/2007: Green's function for the half-space
05/03/2007: Energy methods
07/03/2007: Heat equation: fundamental solution, solution formulas
12/03/2007: Mean value formulas for the heat equation, maximum principle
14/03/2007: Maximum principle on unbounded domains
19/03/2007: Regularity
21/03/2007: Energy methods, backward uniqueness
26/03/2007: Wave equation: D'Alembert's formula, energy methods
28/03/2007: Midterm review
11/04/2007: Midterm Exam
16/04/2007: Tools from functional Analysis
18/04/2007: Reaction-Diffusion equation (overview)
23/04/2007: Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation I
25/04/2007: Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation II
30/04/2007: Special topics
02/05/2007: Special topics
07/05/2007: Presentation
09/05/2007: Presentation
14/05/2007: Presentation
16/05/2007: Review for final exam
TBA Final Exam

Last modified: 2007/03/22
This page: http://math.iu-bremen.de/oliver/teaching/iub/spring2007/math362/index.html
Marcel Oliver (m.oliver@iu-bremen.de)