Mathematical Topics in Kinetic Theory (Part III course)

— Part III, michaelmas terms 2010 & 2011 —

Course description (2011-2012)

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6 (soon!)

Example sheet 1 (chapter 2)

Example sheet 2 (chapter 3)

Example sheet 3 (chapter 4)

Example sheet 4 (chapter 5)

Exam paper 2011

Exam paper 2012


Some links:

Some elements of history of Kinetic Theory (up to 2001) from the webpage of Dave Levermore.

Attack of the Boltzmann Brains (Jim Kakalios)

Sources: Some parts of these lecture notes owe a lot to two sets of hand-written lecture notes on kinetic equations written by Laure Saint-Raymond and Laurent Desvillettes, as well as to the lecture notes available online of G. Allaire and F. Golse on transport and diffusion processes. They also inspire from the classical books of R. Glassey, of C. Cercignani, and of C. Cercignani – R. Illner – M. Pulvirenti, as well as from various recent research papers. Many thanks to Otis Chodosh, who typewrote a first latex version of these notes.

2 comments on “Mathematical Topics in Kinetic Theory (Part III course)

  1. Pengwen says:

    In section 1, it uses ft to represent a smooth solution of Vlasov-Poisson system (VPS). I think here t in $ f_t $ as subscript doesn’t mean $ f_t (t,x,v) $ as a function with t fixed, because the solution should be a function with respect to t and t shouldn’t be fixed.

    But in section 4, definition 4.30, weak solution is defined as a family (f_t)_{t∈[0,T]} . I think here t as a subscript certainly means time, i.e. ft has a fixed time t .

    What’s more, in exercise 2 from, problem 2 says that ” if $ f_t $ is a weak solution “, but shouldn’t weak solution be a family?

    I’m very confused.

    • CM says:

      All along the notes f_t=f_t(z) denotes the function z \mapsto f(t,z) (where z is v or (x,v)) for a given time t. This small -but common- abuse of notation in kinetic theory should not be confused with the subscript notation for derivatives used in hyperbolic equations. In the sentence “if f_t is a weak solution” we only emphasize the previous notation, a solution is of course a function of (t,x,v) with no risk of confusion.

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