MAT9380 – Nonlinear Partial Differential Equations
Course description
Course content
The aim of this course is to provide an introduction to modern methods for studying nonlinear partial differential equations. The content of the course, which can change from time to time, is built around some of the following themes: calculus of variations, nonvariational techniques, weak convergence techniques, Hamilton-Jacobi(-Bellman) equations and the theory of viscosity solutions, systems of conservation laws and the theory of shock wave solutions, and the (incompressible/compressible) Navier-Stokes equations.
Learning outcome
Understanding of some modern methods for studying nonlinear partial differential equations.
Admission to the course
PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.
If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.
PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.
Recommended previous knowledge
Basic training in Sobolev space theory and linear partial differential equations, for example as provided by MAT4305 – Partial Differential Equations and Sobolev Spaces I.
Overlapping courses
- 10 credits overlap with MAT4380 – Nonlinear Partial Differential Equations (discontinued).
Teaching
4 hours of lectures/exercises per week.
The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.
Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.
Examination
1 mandatory assignment.
Final oral examination.
In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.
Examination support material
No examination support material is allowed.
Language of examination
Subjects taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.