Displaying similar documents to “Diffusive limit for finite velocity Boltzmann kinetic models.”

Recent results on the Boltzmann equation

Carlo Cercignani (1996)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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In the last few years the theory of the nonlinear Boltzmann equation has witnessed a veritable turrent of contributions, spurred by the basic result of DiPerna and Lions. Here we wish to survey these results with particular attention to some recent developments.

On the interior boundary-value problem for the stationary Povzner equation with hard and soft interactions

Vladislav A. Panferov (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The Povzner equation is a version of the nonlinear Boltzmann equation, in which the collision operator is mollified in the space variable. The existence of stationary solutions in L 1 is established for a class of stationary boundary-value problems in bounded domains with smooth boundaries, without convexity assumptions. The results are obtained for a general type of collision kernels with angular cutoff. Boundary conditions of the diffuse reflection type, as well as the given incoming...

Ageing in the parabolic Anderson model

Peter Mörters, Marcel Ortgiese, Nadia Sidorova (2011)

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

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The parabolic Anderson model is the Cauchy problem for the heat equation with a random potential. We consider this model in a setting which is continuous in time and discrete in space, and focus on time-constant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the long-term temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly...