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Transport equations with partially B V velocities

Nicolas Lerner (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove the uniqueness of weak solutions for the Cauchy problem for a class of transport equations whose velocities are partially with bounded variation. Our result deals with the initial value problem ∂ t u + X u = f , u | t = 0 = g , where X is the vector fieldwith a boundedness condition on the divergence of each vector field a 1 , a 2 . This model was studied in the paper [LL] with a W 1 , 1 regularity assumption replacing our B V hypothesis. This settles partly a question raised in the paper [Am]. We examine the details of the argument of...

Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation

François Bolley, Arnaud Guillin, Florent Malrieu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the approximation of the solution by the particle system. Finally, a transportation inequality...

Trends to equilibrium in total variation distance

Patrick Cattiaux, Arnaud Guillin (2009)

Annales de l'I.H.P. Probabilités et statistiques

This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this end, we give a general upper bound “à la Pinsker” enabling us to study our problem firstly via usual functional inequalities (Poincaré inequality, weak Poincaré,…) and truncation procedure, and secondly through the introduction of new functional inequalities ℐ ψ ....

Turbulent maps and their ω-limit sets

F. Balibrea, C. La Paz (1997)

Annales Polonici Mathematici

One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.

Two classes of Darboux-like, Baire one functions of two variables

Michael J. Evans, Paul D. Humke (2010)

Czechoslovak Mathematical Journal

Among the many characterizations of the class of Baire one, Darboux real-valued functions of one real variable, the 1907 characterization of Young and the 1997 characterization of Agronsky, Ceder, and Pearson are particularly intriguing in that they yield interesting classes of functions when interpreted in the two-variable setting. We examine the relationship between these two subclasses of the real-valued Baire one defined on the unit square.

Two inequalities for series and sums

Horst Alzer (1995)

Mathematica Bohemica

In this paper we refine an inequality for infinite series due to Astala, Gehring and Hayman, and sharpen and extend a Holder-type inequality due to Daykin and Eliezer.

Currently displaying 221 – 240 of 258