Research interests (in Mathematical Analysis)
Hyperbolic systems of conservation laws:
* Uniqueness and stability in the L$^1$ norm of entropic solutions
of the Cauchy problem, built by wave front-tracking approximations.
* Temple class systems: Boundary value problems and applications to
control theory.
* Systems of balance laws.
* Resonant hyperbolic systems of balance laws.
* Non-strictly hyperbolic systems of conservation laws.
* Traffic flow models.
* Nonclassical solutions.
* Numerical schemes.
Viscosity solutions and control theory:
* Characterization of solutions of the Dirichlet problem
for nonlinear degenerate elliptic equations of 2nd order.
* Invariance and viability properties of a closed set for the trajectories
of either a controlled diffusion process or a controlled deterministic
system with disturbances.