FSF3672 Non - Linear Wave Equations 15.0 credits
Content and learning outcomes
Course contents
Local existence and uniqueness of solutions to non-linear wave equations, continuation criteria, Sobolev embedding, characterisations of global hyperbolicity, the constraint equations for Einstein's equations, local existence and uniqueness of solutions to Einstein's equations, existence of a unique maximal Cauchy development of given initial data to Einstein's equations.
Intended learning outcomes
After the course, the student should have a sufficiently deep knowledge of non-linear wave equations to be able to start working on research projects in the area.
Literature and preparations
Specific prerequisites
Prerequisite for the course is a strong knowledge of differential geometry (differential manifolds, tensors, differential forms) corresponding for example to the advanced level course SF2722 “Differential geometry” and the course SF3670, Semi-Riemannian geometry I.
Recommended prerequisites
Equipment
Literature
The course is primarily based on the book “The Cauchy Problem in General Relativity”, European Mathematical Society, 2009, by Hans Ringström. Also used in the course is the book: “Semi-Riemannian Geometry With Applications to Relativity”, Academic Press, Orlando 1983, by Barrett O'Neill.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
Examination
- HEM1 - Home assignments, 15.0 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Homework assignments and oral test or presentation.
Other requirements for final grade
Homework assignments completed, and satisfactory performance at oral test or presentation
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.