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Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
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]Expand
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Asymptotic L1-decay of solutions of the porous medium equation to self-similarity
We consider the flow of gas in an N-dimensional porous medium with initial density v0NxO 0. The density vNx;tO then satisfies the nonlinear degenerate parabolic equa- tion vt E —v m where m> 1 is aExpand
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On Some Properties of Kinetic and Hydrodynamic Equations for Inelastic Interactions
We investigate a Boltzmann equation for inelastic scattering in which the relative velocity in the collision frequency is approximated by the thermal speed. The inelasticity is given by a velocityExpand
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Entropy Dissipation Methods for Degenerate ParabolicProblems and Generalized Sobolev Inequalities
Abstract. We analyse the large-time asymptotics of quasilinear (possibly) degenerate parabolic systems in three cases: 1) scalar problems with confinement by a uniformly convex potential, 2)Expand
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Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states
Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density. Expand
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Long-Time Asymptotics for Strong Solutions¶of the Thin Film Equation
Abstract: In this paper we investigate the large-time behavior of strong solutions to the one-dimensional fourth order degenerate parabolic equation ut=−(uuxxx)x, modeling the evolution of theExpand
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Contractions in the 2-Wasserstein Length Space and Thermalization of Granular Media
An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particlesExpand
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Particle, kinetic, and hydrodynamic models of swarming
We review the state-of-the-art in the modelling of the aggregation and collective behavior of interacting agents of similar size and body type, typically called swarming. Starting withExpand
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Infinite time aggregation for the critical Patlak-Keller-Segel model in ℝ2
We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, weExpand
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Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model
We analyze the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [IEEE Trans. Automat. Control, 52 (2007), pp. 852–862], which describes the collective behavior of an ensemble of organisms, animals or devices. Expand
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