Research Interests:

• Hyperbolic conservation laws and nonlinear wave equations
• Control problems for moving sets, dynamic blocking problems
• Controlled growth and shape optimization in biology
• Modeling and optimization of traffic flow on networks
• Optimal control, non-cooperative games, and applications to economics and finance

Here is my updated list of publications.

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Brief surveys of recent results and open problems

• Research themes on traffic flow on networks
• Results and open questions on dynamic blocking problems

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Read about the $$ prizes which I am offering for the solution of two mathematical problems

• 1 - A mixing problem
• 2 - A blocking problem

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Slides of recent talks

• Optimal control of propagation fronts and moving sets, (SJTU, 2021).


• A posteriori error estimates for approximate solutions to hyperbolic conservation laws, (Paris, 2021).


• On the optimal shape of tree roots and branches, (Toronto, 2018).


• Uniqueness questions for hyperbolic conservation laws, (Oxford, 2018).


• Global solutions of the Burgers-Hilbert equation, (Cambridge, 2018).


• Uniqueness and generic singularities for some classes of nonlinear wave equations (Oxford, 2018)


• Optima and equilibria for a model of traffic flow (2013)
  (animation: Model 1) (animation: Model 2) (animation: instability of Nash equilibrium, Model 2)


• Dynamic blocking problems for a model of fire propagation (Waterloo, 2011)
  (animation: one-spiral strategy) (animation: one-spiral strategy) (animation: non-isotropic case)


• Controlling Lagrangian systems by active constraints (2010)

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Survey papers

• Flows on networks: recent results and perspectives. EMS Surveys in Mathematical Sciences 1 (2014), 47--111 (with S.Canic, M.Garavello, M.Herty, and B.Piccoli)

  
  

• Dynamic blocking problems for a model of fire propagation. In Advances in Applied Mathematics, Modeling, and Computational Science, pp.~11--40. R.Melnik and I.Kotsireas editors. Fields Institute Communications, Springer, New York, 2013.

  
  

• Contractive metrics for nonsmooth evolutions. In: Nonlinear Partial Differential Equations, The Abel Symposium 2010, pp.13-36. H.Holden and K.Karlsen Eds., Springer-Verlag, 2012.

  
  

• Globally optimal and Nash equilibrium solutions for traffic flow on networks. Proceedings of the conference on Hyperbolic Problems: Theory, Numerics and Applications, in Padova 2012. AIMS, 2014.

  
  

• Open questions in the theory of hyperbolic conservation laws. In: Nonlinear Conservation Laws and Applications, pp.1--22. IMA Volumes in Mathematics and its Applications, Vol.153. A.Bressan, G.Q.Chen, M.Lewicka, and D.Wang editors, Springer-Verlag, 2011.

  
  

• Patchy feedbacks for stabilization and optimal control. In Geometric Control and Nonsmooth Analysis, pp.28-64. F.Ancona, A.Bressan, P.Cannarsa, F.H.Clarke and P.Wolenski Eds., World Scientific 2008 (with F.Ancona).

  
  

• Impulsive control of Lagrangian systems and locomotion in fluids, Discr. Cont. Dynam. Syst. 20 (2008), 1-35.

  
  

• Singularities of stabilizing feedbacks, Rend. Sem. Mat. Univ. Pol. Torino 56 (1998), 87-104.

  
  

• Differential inclusions without convexity. A survey of directionally continuous selections, in: Proceedings of the World Congress of Nonlinear Analysts '92, V.Lakshmikantham Ed., W.de Gruyter, Berlin (1996), 2081-2088.