# NMAK16022U  Partial Differential Equations (PDE)

Volume 2018/2019
Education

MSc Programme in Mathematics

Content

A selection from 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

Learning Outcome

Knowledge:
The properties of the PDEs covered in the course

Competencies:

• Understand the characteristics of the different types of PDEs
• Understand concepts such as existence, uniqueness and regularity of solutions to PDEs
• Determine when a certain solution method applies

Skills:

• Solve classical PDEs
• Establish existence, uniqueness and regularity of solutions to certain PDEs

See Absalon for a list of course literature

A knowledge of Lebesgue measure theory and Banach/Hilbert spaces, corresponding to at least the contents of An0, An1 and An2. Additionally, it might be helpful to have had some exposure to the material from a more advanced Analysis course, f.ex. one of either FunkAn or DifFun.
5 hours of lectures and 2 hours of exercises each week for 8 weeks
Credit
7,5 ECTS
Type of assessment
Written examination, 4 hours under invigilation
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Aid
All aids allowed
Marking scale
Censorship form
No external censorship
One internal examiner.
Re-exam

As ordinary exam.

If ten or fewer students have signed up for re-exam, the type of assessment will be changed to a 30 min. oral exam with 30 min preparation. All aids allowed during preparation time, none for the examination. Several internal examiners.

##### Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

• Category
• Hours
• Lectures
• 40
• Exercises
• 16
• Exam
• 4
• Preparation
• 146
• Total
• 206