Displaying similar documents to “Generalized variational principles”

Kinetic and hydrodynamic equations for granular media

Mario Pulvirenti (1999)

Journées équations aux dérivées partielles

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In this lecture i present some open mathematical problems concerning some PDE arising in the study of one-dimensional models for granular media.

Collision probabilities in the rarefaction fan of asymmetric exclusion processes

Pablo A. Ferrari, Patricia Gonçalves, James B. Martin (2009)

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

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We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate ∈(1/2, 1] and to the left at rate 1−, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose...

Many-body aspects of approach to equilibrium

Eric Carlen, M. C. Carvalho, Michael Loss (2000)

Journées équations aux dérivées partielles

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Kinetic theory and approach to equilibrium is usually studied in the realm of the Boltzmann equation. With a few notable exceptions not much is known about the solutions of this equation and about its derivation from fundamental principles. In 1956 Mark Kac introduced a probabilistic model of N interacting particles. The velocity distribution is governed by a Markov semi group and the evolution of its single particle marginals is governed (in the infinite particle limit) by a caricature...

On measure solutions to the Zero-pressure gas model and their uniqueness

Jiequan Li, Gerald G. Warnecke (2002)

Mathematica Bohemica

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The system of zero-pressure gas dynamics conservation laws describes the dynamics of free particles sticking under collision while mass and momentum are conserved. The existence of such solutions was established some time ago. Here we report a uniqueness result that uses the Oleinik entropy condition and a cohesion condition. Both of these conditions are automatically satisfied by solutions obtained in previous existence results. Important tools in the proof of uniqueness are regularizations,...