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Pré-Publication, Document De Travail Année : 2013

Fractional Fokker-Planck equation

Résumé

This paper deals with the long time behavior of solutions to a "fractional Fokker-Planck" equation of the form $\partial_t f = I[f] + \text{div}(xf)$ where the operator $I$ stands for a fractional Laplacian. We prove an exponential in time convergence towards equilibrium in new spaces. Indeed, such a result was already obtained in a $L^2$ space with a weight prescribed by the equilibrium in \cite{GI}. We improve this result obtaining the convergence in a $L^1$ space with a polynomial weight. To do that, we take advantage of the recent paper \cite{GMM} in which an abstract theory of enlargement of the functional space of the semigroup decay is developed.
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Dates et versions

hal-00914059 , version 1 (04-12-2013)
hal-00914059 , version 2 (23-10-2014)

Identifiants

Citer

Isabelle Tristani. Fractional Fokker-Planck equation. 2014. ⟨hal-00914059v2⟩
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