195 citations · 452 across the 18 of their papers we have counts for
19 papers
Variational derivation of the homogeneous Boltzmann equation
Giada Basile, Dario Benedetto, Carlo Orrieri
We introduce a variational formulation of the homogeneous Boltzmann equation, with hard-sphere cross section, which selects the unique energy conserving solution. We prove that thi…
Entropy dissipation inequality for general binary collision models
Giada Basile, Dario Benedetto
We introduce a ``two-particle factorization'' condition which allows us to formulate the homogeneous Boltzmann equation for non-reversible collision kernels in terms of an entropy…
Large time analysis of the rate function associated to the Boltzmann equation: dynamical phase transitions
Giada Basile, Dario Benedetto, Lorenzo Bertini +1
We analyse the large time behaviour of the rate function that describes the probability of large fluctuations of an underlying microscopic model associated to the homogeneous Boltz…
Asymptotic probability of energy increasing solutions to the homogeneous Boltzmann equation
Giada Basile, Dario Benedetto, Lorenzo Bertini +1
Weak solutions to the homogeneous Boltzmann equation with increasing energy have been constructed by Lu and Wennberg. We consider an underlying microscopic stochastic model with bi…
Large deviations for a binary collision model: energy evaporation
Giada Basile, Dario Benedetto, Lorenzo Bertini +1
We analyze the large deviations for a discrete energy Kac-like walk. In particular, we exhibit a path, with probability exponentially small in the number of particles, that looses…
Large deviations for Kac-like walks
Giada Basile, Dario Benedetto, Lorenzo Bertini +1
We introduce a Kac's type walk whose rate of binary collisions preserves the total momentum but not the kinetic energy. In the limit of large number of particles we describe the dy…