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General


Description

The aim of this course is to provide an introduction to the theory of hyperbolic conservation laws and their perturbations with emphasis on integrability aspects, singularity of their solutions in relation to catastrophe theory and phase transitions.
Specific application of conservation laws methods to mean field models in statistical thermodynamics will be also discussed.

Semester

Autumn 2018 (Monday, October 8 to Friday, December 14)

Hours

  • Live lecture hours: 10
  • Recorded lecture hours: 0
  • Total advised study hours: 40

Timetable

  • Tue 13:05 - 13:55

Prerequisites

No specific requirements. Standard undergraduate courses in analysis, mathematical methods and partial differential equations are desirable.

Syllabus

1) Introduction to hyperbolic conservation laws of hydrodynamic type
2) Integrability and generalised hodograph method
3) Singularities and catastrophes
4) Viscous and dispersive regularisations
5) Critical asymptotics and Universality
6) Mean field models and equations of state

Bibliography


Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theoryB A Dubrovin and S P Novikov
Hyperbolic systems of conservation lawsAlberto Bressan
Singularity Theory and an introduction to Catastrophe TheoryYung-Chen Lu
Catastrophe theoryV.I. Arnold
Dispersive and diffusive-dispersive shock waves for non-convex conservation lawsG.A. El, M.A. Hoefer, M.Shearer
Introduction to phase transitions and critical phenomenaH.E. Stanley


Note:

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Assessment



Assessment for this course consists of a paper with a set of 4 questions marked out of 100points. Each question is split in two subquestions and it is worth overall 25points. The exam paper covers a selection of topics from the course.
Marking scheme will be provided at the end of the examination period.

No assignments have been set for this course.

Recorded Lectures


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