5 papers
Diffusion Approximations of Markovian Solutions to Discontinuous ODEs
Alberto Bressan, Marco Mazzola, Khai T. Nguyen
In a companion paper, the authors have characterized all deterministic semigroups, and all Markov semigroups, whose trajectories are Carathe'odory solutions to a given ODE x'=f(x),…
Markovian Solutions to Discontinuous ODEs
Alberto Bressan, Marco Mazzola, Khai T. Nguyen
Given a possibly discontinuous, bounded function , we consider the set of generalized flows, obtained by assigning a probability measure on the set o…
Approximation of Sweeping Processes and Controllability for a Set Valued Evolution
Alberto Bressan, Marco Mazzola, Khai T. Nguyen
We consider a controlled evolution problem for a set , originally motivated by a model where a dog controls a flock of sheep. Necessary conditions and sufficie…
Lyapunov's theorem via Baire category
Marco Mazzola, Khai T. Nguyen
Lyapunov's theorem is a classical result in convex analysis, concerning the convexity of the range of nonatomic measures. Given a family of integrable vector functions on a compact…
Global generalized characteristics for the Dirichlet problem for Hamilton-Jacobi equations at a supercritical energy level
Piermarco Cannarsa, Wei Cheng, Marco Mazzola +1
We study the nonhomogeneous Dirichlet problem for first order Hamilton-Jacobi equations associated with Tonelli Hamiltonians on a bounded domain of assuming the energy l…