Fall Semester 2004

Partial Differential Equations


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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:  M 15:00, W 11:00 in Research I, 107
Grader:Shaowu Tang

Time and Place:
Lectures:  Tu 9:45-11:00, Th 8:15--9:30 in East Hall 8

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


Class Schedule (subject to change!)

31/08/2004: No class
02/09/2004: Introduction; linear transport equation
07/09/2004: Laplace equation, fundamental solution
09/09/2004: Poisson equation, mean value formulas
14/09/2004: Harmonic functions: maximum principle, uniqueness for solutions to the Poisson equation, regularity
16/09/2004: Harmonic functions: analyticity
21/09/2004: Harmonic functions: Liouville's theorem, Harnack's inequality
23/09/2004: Dirichlet problem, Green's functions
28/09/2004: Green's function for the half-space; energy methods
30/09/2004: Heat equation: fundamental solution, solution formulas
05/10/2004: Mean value formulas for the heat equation, maximum principle
07/10/2004: Regularity
12/10/2004: Energy methods, backward uniqueness
14/10/2004: Wave equation: D'Alembert's formula, energy methods
19/10/2004: Tools from functional Analysis I
21/10/2004: Tools from functional Analysis II
26/10/2004: Midterm review
28/10/2004: Midterm Exam
02/11/2004: Reaction-Diffusion equation (overview)
04/11/2004: Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation I
09/11/2004: Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation II
11/11/2004: Special topics
16/11/2004: Special topics
18/11/2004: Special topics
23/11/2004: Presentation
25/11/2004: Presentation
30/11/2004: Presentation
02/12/2004: Review for final exam
09/12/2004: Final Exam, 11:00-13:00 in the Research II Lecture Hall

Last modified: 2004/09/29
This page: http://math.iu-bremen.de/oliver/teaching/iub/fall2004/pde/pde.html
Marcel Oliver (m.oliver@iu-bremen.de)