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Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates.

José A. Carrillo, Robert J. McCann, Cédric Villani (2003)

Revista Matemática Iberoamericana

The long-time asymptotics of certain nonlinear , nonlocal, diffusive equations with a gradient flow structure are analyzed. In particular, a result of Benedetto, Caglioti, Carrillo and Pulvirenti [4] guaranteeing eventual relaxation to equilibrium velocities in a spatially homogencous model of granular flow is extended and quantified by computing explicit relaxation rates. Our arguments rely on establishing generalizations of logarithmic Sobolev inequalities and mass transportation inequalities,...

Kirchhoff-Carrier elastic strings in noncylindrical domains.

Limaco Ferrel, J., Medeiros, L.A. (1999)

Portugaliae Mathematica

Klassische Lösungen im Großen semilinearen parabolischer Differentialgleichungen.

Wolf von Wahl, Hartmut Pecher (1975)

Mathematische Zeitschrift

Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator

Robert Haller-Dintelmann, Julian Wiedl (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Replacing the gaussian semigroup in the heat kernel estimates by the Ornstein-Uhlenbeck semigroup on $ℝ^{d}$ , we define the notion of Kolmogorov kernel estimates. This allows us to show that under Dirichlet boundary conditions Ornstein-Uhlenbeck operators are generators of consistent, positive, (quasi-) contractive $C_{0}$ -semigroups on $L^{p} (Ω)$ for all $1 \leq p < \infty$ and for every domain $Ω \subseteq ℝ^{d}$ . For exterior domains with sufficiently smooth boundary a result on the location of the spectrum of these operators is also given.

Krylov subspace spectral methods for variable-coefficient initial-boundary value problems.

Lambers, James V. (2005)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]