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The first author acknowledges fruitful discussions with L. Gross and D. Stroock, the second author with D. Bakry, and the second and third authors interactions with C. Villani. Also we thank the anonymous referee for his extremely constructive comments. Abstract It is well known that the analysis of the large-time asymptotics of Fokker-Planck type equations(More)
The classical Csiszz ar{Kullback inequality bounds the L 1 {distance of two probability densities in terms of their relative (convex) entropies. Here we generalize such inequalities to not necessarily normalized and possibly non-positive L 1 functions. Also, our generalized Csiszz ar{Kullback inequalities are in many important cases sharper than the(More)
We analyze the large-time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced in the pertinent literature in recent years. As specific examples, we study models with fixed saving propensity introduced by A. Chakraborty and B.K. Chakrabarthi [11], as well as models involving both exchange between agents(More)
The long-time asymptotics of solutions of the viscous quantum hydrodynamic model in one space dimension is studied. This model consists of continuity equations for the particle density and the current density, coupled to the Poisson equation for the electrostatic potential. The equations are a dispersive and viscous regularization of the Euler equations. It(More)
Many transport equations, such as the neutron transport, radiative transfer, and transport equations for waves in random media, have a diiusive scaling that leads to the diiusion equations. In many physical applications, the scaling parameter (mean free path) may diier in several orders of magnitude from the rareeed regimes to the hydrodynamic (diiusive)(More)
We prove the global existence of nonnegative variational solutions to the " drift diffusion " evolution equation ∂tu + div " u " 2D ∆ √ u √ u − f " « = 0 under variational boundary condition. Despite the lack of a maximum principle for fourth order equations, nonnegative solutions can be obtained as a limit of a variational approximation scheme by(More)
We introduce and discuss certain kinetic models of (continuous) opinion formation involving both exchange of opinion between individual agents and diffusion of information. We show conditions which ensure that the kinetic model reaches non trivial stationary states in case of lack of diffusion in correspondence of some opinion point. Analytical results are(More)