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FSF3672 Non - Linear Wave Equations 15.0 credits

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus FSF3672 (Spring 2019–) are denoted with an asterisk ( )

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

No information inserted

Equipment

No information inserted

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

P, F

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

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

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.

Further information

Course room in Canvas

Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.

Offered by

Main field of study

This course does not belong to any Main field of study.

Education cycle

Third cycle

Add-on studies

No information inserted

Contact

Mattias Dahl (dahl@math.kth.se), Hans Ringström (hansr@kth.se)

Postgraduate course

Postgraduate courses at SCI/Mathematics