206 citations · 1.1k across the 65 of their papers we have counts for
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Fokker--Planck equations and n--dimensional Poincaré inequalities for isotropic densities
G. Furioli, A. Pulvirenti, E. Terraneo +1
We consider new connections between the problem of trend to equilibrium for the n-dimensional Fokker--Planck equation of statistical physics, and weighted Poincaré inequality. To t…
Impact of interaction forces in first order many-agent systems for swarm manufacturing
Ferdinando Auricchio, Massimo Carraturo, Giuseppe Toscani +1
We study the large time behavior of a system of interacting agents modeling the relaxation of a large swarm of robots, whose task is to uniformly cover a portion of the domain by c…
Trends to equilibrium for a nonlocal Fokker-Planck equation
Ferdinando Auricchio, Giuseppe Toscani, Mattia Zanella
We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of…
Non-Maxwellian kinetic equations modeling the evolution of wealth distribution
Giulia Furioli, Ada Pulvirenti, Elide Terraneo +1
We introduce a class of new one-dimensional linear Fokker--Planck type equations describing the evolution in time of the wealth in a multi-agent society. The equations are obtained…
Nonlinear diffusions: extremal properties of Barenblatt profiles, best matching and delays
Jean Dolbeault, Giuseppe Toscani
In this paper, we consider functionals based on moments and non-linear entropies which have a linear growth in time in case of source-type so-lutions to the fast diffusion or porou…
Stability results for logarithmic Sobolev and Gagliardo-Nirenberg inequalities
Jean Dolbeault, Giuseppe Toscani
This paper is devoted to improvements of functional inequalities based on scalings and written in terms of relative entropies. When scales are taken into account and second moments…
Best matching Barenblatt profiles are delayed
Jean Dolbeault, Giuseppe Toscani
The growth of the second moments of the solutions of fast diffusion equations is asymptotically governed by the behavior of self-similar solutions. However, at next order, there is…
Renyi entropy and improved equilibration rates to self-similarity for nonlinear diffusion equations
J. A. Carrillo, G. Toscani
We investigate the large-time asymptotics of nonlinear diffusion equations in dimension , in the exponent interval , when the initial datum …
Condensation phenomena in nonlinear drift equations
Jose' A. Carrillo, Marco Di Francesco, Giuseppe Toscani
We study nonnegative, measure-valued solutions to nonlinear drift type equations modelling concentration phenomena related to Bose-Einstein particles. In one spatial dimension, we…
Large-time Behavior of the Solutions to Rosenau Type Approximations to the Heat Equation
Thomas Rey, Giuseppe Toscani
In this paper we study the large-time behavior of the solution to a general Rosenau type approximation to the heat equation, by showing that the solution to this approximation appr…
Improved interpolation inequalities, relative entropy and fast diffusion equations
Jean Dolbeault, Giuseppe Toscani
We consider a family of Gagliardo-Nirenberg-Sobolev interpolation inequalities which interpolate between Sobolev's inequality and the logarithmic Sobolev inequality, with optimal c…
The grazing collision limit of the inelastic Kac model around a Lévy-type equilibrium
G. Furioli, A. Pulvirenti, E. Terraneo +1
This paper is devoted to the grazing collision limit of the inelastic Kac model introduced in [A. Pulvirenti and G. Toscani. J. Statist. Phys., 114(5-6):1453--1480, 2004], when the…
Measure valued solutions of sub-linear diffusion equations with a drift term
S. Fornaro, S. Lisini, G. Savare' +1
In this paper we study nonnegative, measure valued solutions of the initial value problem for one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by…
Self-similarity and power-like tails in nonconservative kinetic models
L. Pareschi, G. Toscani
In this paper, we discuss the large--time behavior of solution of a simple kinetic model of Boltzmann--Maxwell type, such that the temperature is time decreasing and/or time increa…
Fast diffusion equations: matching large time asymptotics by relative entropy methods
Jean Dolbeault, Giuseppe Toscani
A non self-similar change of coordinates provides improved matching asymptotics of the solutions of the fast diffusion equation for large times, compared to already known results,…
The grazing collision limit of Kac caricature of Bose-Einstein particles
Thibaut Allemand, Giuseppe Toscani
We discuss the grazing collision limit of certain kinetic models of Bose-Einstein particles obtained from a suitable modification of the one- dimensional Kac caricature of a Maxwel…
Strong Convergence towards self-similarity for one-dimensional dissipative Maxwell models
G. Furioli, A. Pulvirenti, E. Terraneo +1
We prove the propagation of regularity, uniformly in time, for the scaled solutions of one-dimensional dissipative Maxwell models. This result together with the weak convergence to…
Relaxation rate, diffusion approximation and Fick's law for inelastic scattering Boltzmann models
Bertrand Lods, Clément Mouhot, Giuseppe Toscani
We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, w…
Over-populated Tails for conservative-in-the-mean Inelastic Maxwell Models
José Antonio Carrillo, Stéphane Cordier, Giuseppe Toscani
We introduce and discuss spatially homogeneous Maxwell-type models of the nonlinear Boltzmann equation undergoing binary collisions with a random component. The random contribution…
On a kinetic model for a simple market economy
Stephane Cordier, Lorenzo Pareschi, Giuseppe Toscani
In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quas…