Faculty of Science

Partial Differential Equations (PDE)
Provider: Faculty of Science

Activity no.: 5583-19-07-31
	Enrollment deadline: 28/08/2019

Place

Department of Mathematical Sciences

Date and time

02.09.2019, at: 09:00 - 08.11.2019, at: 16:00

Regular seats

ECTS credits

7.50

Contact person

Nina Weisse E-mail address: weisse@math.ku.dk

Enrolment Handling/Course Organiser

Niels Martin Møller E-mail address: nmoller@math.ku.dk

Teaching language

English partially in English

Semester/Block

Block 1

Scheme group

Exam form

Written examination, 4 hours under invigilation

Exam form

Written examination, 4 hours under invigilation

Exam details

Marking scale 7-point grading scale Censorship form No external censorship One internal examiner.

Course workload

Course workload category	Hours
Lectures	40.00
Exercises	16.00
Exam	4.00
Preparation	146.00

Sum	206.00

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

Literature

See Absalon for a list of course literature

Teaching and learning methods

5 hours of lectures and 2 hours of exercises each week for 8 weeks.

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