Undergraduate Course: Analysis of Nonlinear Waves (MATH11093)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 4 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | Fundamental theorem of ordinary differential equations, the contraction mapping principle. Duhamel's formula, PDEs as Euler-Lagrange equations and Noether's theorem, continuous functions as a normed vector space, completion of a metric space, Lebesgue and Sobolev spaces, Sobolev embedding theorem, existence and uniqueness of solutions, methods for proving blow up.
Aims :
1. To explore the concepts of local and global solutions and of blow up for ordinary and partial differential equations.
2. To introduce the relevant sets of functions to study nonlinear evolution equations and show how they are used.
3. To construct solutions to nonlinear wave equations. |
| Course description |
See short description.
See short description.
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Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
1. Understand local wellposedness.
2. Ability to calculate conserved quantities using Noether's theorem.
3. Ability to use contraction mapping theorem.
4. Familiarity with function spaces.
5. Understand global existence and blow up and the ability to determine which in common cases.
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Reading List
Evans, L C, Partial differential equations (American Mathematical Society, 1998)
John, F, Nonlinear wave equations: formation of sigularities (American Mathematical Society, 1990)
Racke, R, Lectures on Nonlinear Evolution Equations: Initial value problems (Vieweg, 1992) |
Contacts
| Course organiser | Dr Pieter Blue
Tel: (0131 6)50 5076
Email: P.Blue@ed.ac.uk |
Course secretary | Mrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk |
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