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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)

This note is concerned with intermediate inequalities which interpolate between the logarithmic Sobolev and the Poincaré inequalities. For such generalized Poincaré inequalities we improve upon the known constants from the literature. 1. Introduction In 1989 W. Beckner [B] derived a family of generalized Poincaré inequalities (GPI) for the Gaussian measure… (More)

- A. Arnold, J. A. Carrillo
- 1999

This paper is concerned with scaling limits in kinetic semiconductor models. For the classical Vlasov-Poisson-Fokker-Planck equation and its quantum mechanical counterpart, the Wigner-Poisson-Fokker-Planck equation, three distinguished scaling regimes are presented. Using Hilbert and Chapman-Enskog expansions, we derive two drift-diiusion type… (More)

This paper is concerned with transparent boundary conditions (TBCs) for the time–dependent Schrödinger equation on a circular domain. Discrete TBCs are introduced in the numerical simulations of problems on unbounded domains in order to reduce the computational domain to a finite region in order to make this problem feasible for numerical simulations. The… (More)

The analysis of dissipative transport equations within the framework of open quantum systems with Fokker–Planck–type scattering is carried out from the perspective of a Wigner function approach. In particular, the well–posedness of the self–consistent whole–space problem in 3D is analyzed: existence of solutions, uniqueness and asymptotic behavior in time,… (More)

- René Hammer, Walter Pötz, Anton Arnold
- J. Comput. Physics
- 2014

This paper is concerned with the one-dimensional stationary linear Wigner equation, a kinetic formulation of quantum mechanics. Specifically , we analyze the well-posedness of the boundary value problem on a slab of the phase-space with given inflow data for a discrete-velocity model. We find that the problem is uniquely solvable if zero is not a discrete… (More)

- A. Arnold, M. Ehrhardt
- 1998

This paper is concerned with transparent boundary conditions (TBCs) for wide angle \parabolic" equations (WAPEs) in underwater acoustics (assuming cylindrical symmetry). Existing discretizations of these TBCs introduce slight numerical reeections at this arti-cial boundary and also render the overall Crank{Nicolson nite diierence method only conditionally… (More)

We consider a polymeric fluid model, consisting of the incompressible Navier-Stokes equations coupled to a non-symmetric Fokker-Planck equation. First, steady states and exponential convergence to them in relative entropy are proved for the linear Fokker-Planck equation in the Hookean case. The FENE model is also addressed proving the existence of… (More)