Fall Semester 2008

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:  Mo, Fr 11:15 in Research I, 107
Grader:Mahmut Çalik

Time and Place:
Lectures:  We, Fr 9:45 in East Hall 3

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


Class Schedule (subject to change!)

03/09/2008: Introduction; linear transport equation
05/09/2008: Laplace equation, fundamental solution
10/09/2008: Poisson equation, mean value formulas
12/09/2008: Harmonic functions: maximum principle, uniqueness for solutions to the Poisson equation, regularity
17/09/2008: Harmonic functions: analyticity
19/09/2008: Harmonic functions: Liouville's theorem, Harnack's inequality
24/09/2008: Dirichlet problem, Green's functions
26/09/2008: Green's function for the half-space; energy methods
01/10/2008: Heat equation: fundamental solution, solution formulas
08/10/2008: Mean value formulas for the heat equation, maximum principle
10/10/2008: Maximum principle on unbounded domains
15/10/2008: Regularity
17/10/2008: Energy methods, backward uniqueness
22/10/2008: Wave equation: D'Alembert's formula, energy methods
24/10/2008: Midterm review
29/10/2008: Midterm Exam
31/10/2008: Midterm return and discussion
05/11/2008: Tools from Functional Analysis
07/11/2008: Reaction-Diffusion equations (overview)
12/11/2008: Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation I
14/11/2008: Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation II
19/11/2008: Proof of existence and uniqueness of solutions to the Fisher-Kolmogorov equation III
21/11/2008: Introduction to scalar conservation laws I
26/11/2008: Introduction to scalar conservation laws II
28/11/2008: Presentation
03/12/2008: Presentation
05/12/2008: Review for final exam
11/12/2008: Final Exam, 13:00-15:00 in East Hall 4

Last modified: 2008/11/27
This page: http://math.jacobs-university.de/oliver/teaching/jacobs/fall2008/math362/index.html
Marcel Oliver (m.oliver@jacobs-university.de)