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Partial Differential Equations (PDE)
Provider: Faculty of Science

Activity no.: 5583-21-07-31 
Enrollment deadline: 06/09/2021
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time06.09.2021, at: 08:00 - 14.11.2021, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserNiels Martin Møller    E-mail address: nmoller@math.ku.dk
Teaching languageEnglish partially in English
Semester/BlockBlock 1
Scheme groupB
Exam formWritten examination, 4 hours under invigilation
Exam formWritten examination, 4 hours under invigilation
Grading scale7 point grading scale. For PhD students: Passed / Not Passed
Course workload
Course workload categoryHours
Lectures40.00
Exercises16.00
Exam4.00
Preparation146.00

Sum206.00


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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All planned PhD courses at the PhD School are visible in the course catalogue. Courses are published regularly.