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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 2019 (Monday, October 7 to Friday, December 13)

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

Other courses that you may be interested in:

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



No assessment information is available yet.

No assignments have been set for this course.

Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
1MAGIC097_Lecture1.pdfL
2MAGIC097_Lecture2.pdfL


Recorded Lectures


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