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
Brief surveys of recent results and open problems
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)
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.