Displaying similar documents to “Large time behaviour of solutions to nonhomogeneous diffusion equations”

Sobolev-Kantorovich Inequalities

Michel Ledoux (2015)

Analysis and Geometry in Metric Spaces

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In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds...

Optimal heat kernel bounds under logarithmic Sobolev inequalities

Dominique Bakry, Daniel Concordet, Michel Ledoux (2010)

ESAIM: Probability and Statistics

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We establish optimal uniform upper estimates on heat kernels whose generators satisfy a logarithmic Sobolev inequality (or entropy-energy inequality) with the optimal constant of the Euclidean space. Off-diagonals estimates may also be obtained with however a smaller d istance involving harmonic functions. In the last part, we apply these methods to study some heat kernel decays for diffusion operators of the type Laplacian minus the gradient of a smooth potential with a given...

Logarithmic Sobolev inequalities for inhomogeneous Markov Semigroups

Jean-François Collet, Florent Malrieu (2008)

ESAIM: Probability and Statistics

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We investigate the dissipativity properties of a class of scalar second order parabolic partial differential equations with time-dependent coefficients. We provide explicit condition on the drift term which ensure that the relative entropy of one particular orbit with respect to some other one decreases to zero. The decay rate is obtained explicitly by the use of a Sobolev logarithmic inequality for the associated semigroup, which is derived by an adaptation of Bakry's -calculus. As...

On Entropy Bumps for Calderón-Zygmund Operators

Michael T. Lacey, Scott Spencer (2015)

Concrete Operators

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We study twoweight inequalities in the recent innovative language of ‘entropy’ due to Treil-Volberg. The inequalities are extended to Lp, for 1 < p ≠ 2 < ∞, with new short proofs. A result proved is as follows. Let ℇ be a monotonic increasing function on (1,∞) which satisfy [...] Let σ and w be two weights on Rd. If this supremum is finite, for a choice of 1 < p < ∞, [...] then any Calderón-Zygmund operator T satisfies the bound [...]

Exponential convergence to equilibrium Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics

Marzia Bisi, Laurent Desvillettes, Giampiero Spiga (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We show that the entropy method, that has been used successfully in order to prove exponential convergence towards equilibrium with explicit constants in many contexts, among which reaction-diffusion systems coming out of reversible chemistry, can also be used when one considers a reaction-diffusion system corresponding to an irreversible mechanism of dissociation/recombination, for which no natural entropy is available.