http://www.cnr.it/ontology/cnr/individuo/prodotto/ID224074

On the minimization problem of sub-linear convex functionals (Articolo in rivista)

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On the minimization problem of sub-linear convex functionals (Articolo in rivista) (literal)

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Ben Abdallah, Naoufel; Gamba, Irene M.; Toscani, Giuseppe (2011)
On the minimization problem of sub-linear convex functionals
in Kinetic & related models; American Institute of Mathematical Sciences, Springfield [MO] (Stati Uniti d'America)
(literal)

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Laboratoire MIP, University Paul Sabatier, Toulouse, France; ICES and Department of Mathematics and ICES, University of Texas, Austin, TX, United States; Università di Pavia, Dipartimento di Matematica, Pavia. (literal)

Titolo

Abstract

The study of the convergence to equilibrium of solutions to Fokker-Planck type equations with linear diffusion and super-linear drift leads in a natural way to a minimization problem for an energy functional (entropy) which relies on a sub-linear convex function. In many cases, conditions linked both to the non-linearity of the drift and to the space dimension allow the equilibrium to have a singular part. We present here a simple proof of existence and uniqueness of the minimizer in the two physically interesting cases in which there is the constraint of mass, and the constraints of both mass and energy. The proof includes the localization in space of the (eventual) singular part. The major example is related to the Fokker-Planck equation introduced in [6, 7] to describe the evolution of both Bose-Einstein and Fermi-Dirac particles. (literal)

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