Partial Differential Equations (PDE)

Course description

Content

The course is structured around the following list of subjects:

The classical PDEs:

• Laplace's equation
• The heat equation
• The wave equation

 Second order linear elliptic PDEs:

• Existence of weak solutions
• Regularity
• Maximum principles

 Second order linear parabolic PDEs:

• Existence of weak solutions
• Regularity
• Maximum principles

 Second order linear hyperbolic PDEs:

• Existence of weak solutions
• Regularity
• Propagation of singularities

Nonlinear PDEs:

• The Calculus of Variations
• Fixed point methods
• Method of sub-/supersolutions
• Non-existence of solutions

Recommended academic qualifications

A knowledge of real analysis, Lebesgue measure theory, L^p spaces and basic theory of Banach/Hilbert spaces, corresponding to at least the contents of the following courses:

- Analyse 0 (An0), and
- Analyse 1 (An1), and
- Lebesgueintegralet og målteori (LIM), or alternatively Analyse 2 (An2) from previous years.
- Advanced Vector Spaces (AdVec), which may be taken simultaneously with (PDEs), or alternatively Functional Analysis (FunkAn).

Having academic qualifications equivalent to a BSc degree is recommended.