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Lecture Notes

  • Hyperbolic conservation laws: an illustrated tutorial.
    Notes for a summer course, Cetraro 2009 (81 pages).

  • Viscosity solutions of Hamilton-Jacobi equations and optimal control problems
    An illustrated tutorial. Original version: Trondheim, NTNU 2001. Revised: Shanghai Jiao Tong University, 2011 (56 pages).

  • Noncooperative differential games.
    Notes for a summer course, Padova 2010 (81 pages).

  • Lecture Notes on the Center Manifold Theorem
    S.I.S.S.A., 2003 (16 pages).

  • Notes on the Boltzmann equation
    Lecture notes for a summer course, S.I.S.S.A. 2005 (28 pages).

  • BV solutions to hyperbolic system by vanishing viscosity
    Lecture notes for a C.I.M.E. course, 2003 (77 pages).

  • Symmetries and blow up patterns
    A short tutorial, S.I.S.S.A. 1999 (17 pages).


  • Slides of tutorials

  • A tutorial on hyperbolic systems of conservation laws in one space dimension
    I - Basic concepts
    II - The Cauchy problem
    III - Uniqueness, continuous dependence, and viscous approximations

  • Control Theory: a brief tutorial

  • An introduction to noncooperative games

  • Conservation law models for traffic flow

  • Dynamic blocking problems

  • Controlling Lagrangian systems by active constraints