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ASYMPTOTICS OF THE FAST DIFFUSION EQUATION VIA ENTROPY ESTIMATES
"... Abstract. We consider nonnegative solutions of the fast diffusion equation ut = ∆u m with m ∈ (0, 1), in the Euclidean space R d, d ≥ 3, and study the asymptotic behavior of a natural class of solutions, in the limit corresponding to t → ∞ for m ≥ mc = (d−2)/d, or as t approaches the extinction ti ..."
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Cited by 14 (7 self)
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Abstract. We consider nonnegative solutions of the fast diffusion equation ut = ∆u m with m ∈ (0, 1), in the Euclidean space R d, d ≥ 3, and study the asymptotic behavior of a natural class of solutions, in the limit corresponding to t → ∞ for m ≥ mc = (d−2)/d, or as t approaches the extinction time when m < mc. For a class of initial data we prove that the solution converges with a polynomial rate to a selfsimilar solution, for t large enough if m ≥ mc, or close enough to the extinction time if m < mc. Such results are new in the range m ≤ mc where previous approaches fail. In the range mc < m < 1 we improve on known results. 1.
TRANSPORT INEQUALITIES. A SURVEY
"... Abstract. This is a survey of recent developments in the area of transport inequalities. We investigate their consequences in terms of concentration and deviation inequalities and sketch their links with other functional inequalities and also large deviation theory. ..."
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Cited by 7 (1 self)
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Abstract. This is a survey of recent developments in the area of transport inequalities. We investigate their consequences in terms of concentration and deviation inequalities and sketch their links with other functional inequalities and also large deviation theory.
A new characterization of Talagrand’s transportentropy inequalities and applications
, 2011
"... We give a characterization of transportentropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley–Stroock perturbation lemma). ..."
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Cited by 3 (3 self)
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We give a characterization of transportentropy inequalities in metric spaces. As an application we deduce that such inequalities are stable under bounded perturbation (Holley–Stroock perturbation lemma).
SLOW DECAY OF GIBBS MEASURES WITH HEAVY TAILS
, 811
"... Abstract. We consider Glauber dynamics reversible with respect to Gibbs measures with heavy tails. Spins are unbounded. The interactions are bounded and finite range. The self potential enters into two classes of measures, κconcave probability measure and subexponential laws, for which it is known ..."
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Abstract. We consider Glauber dynamics reversible with respect to Gibbs measures with heavy tails. Spins are unbounded. The interactions are bounded and finite range. The self potential enters into two classes of measures, κconcave probability measure and subexponential laws, for which it is known that no exponential decay can occur. We prove, using coercive inequalities, that the associated infinite volume semigroup decay to equilibrium polynomially and stretched exponentially, respectively. Thus improving and extending previous results by Bobkov and Zegarlinski. 1.