Postgraduate Course: MIGS: Advanced PDE 2 (MATH12026)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 12 (Postgraduate) |
Availability | Not available to visiting students |
| SCQF Credits | 15 |
ECTS Credits | 7.5 |
| Summary | The course will cover the basic techniques and methods needed for a rigorous understanding of Hyperbolic, Schrodinger and Hamiltonian-Jacobi equations. |
| Course description |
i. Heat and Schrodinger equations: Initial value problem and generalised solutions. Nonlinear Schrodinger Equation and Strictarz estimates.
ii. Hyperbolic Equations: Continuity and existence of weak solutions,
iii. Variational techinques: Euler-Lagrange equations, existence of minimisers and critical points.
iv. Nonvarational techiniques: Monotonicity methods, Fix point methods, Gradient flows.
v. Hamiltonion-Jacobi Equations: Definition and uniqueness of viscosity solutions, control theory and the Hopf-Lax formula.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- Thoroughly understand the basic properties of Hyperbolic Partial Differential Equations.
- Demonstrate familiarity with Schrodinger Equations and Streictarz inequalities.
- Demonstrate concrete understanding of basic concepts and tools needed to analyse Hyperbolic, Schrodinger and Hamiltonian-Jacobi Equations rigorously.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Not entered |
Contacts
| Course organiser | Prof Benedict Leimkuhler
Tel:
Email: B.Leimkuhler@ed.ac.uk |
Course secretary | Mrs Katy Cameron
Tel:
Email: Katy.Cameron@ed.ac.uk |
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