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Probabilistic interpretation
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A Gradient Flow Approach to Kinetic Equations
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- 1 Intro
- 2 Contents
- 3 A current-density formulation of the heat equation
- 4 Variational characterization
- 5 Heat equation in probability space
- 6 Comments
- 7 Linear Boltzmann equations
- 8 Probabilistic interpretation
- 9 Boltzmann-Grad limit of the Lorentz gas
- 10 Rayleigh-Boltzmann equation
- 11 Linear phonon Boltzmann equation
- 12 A current-measure formulation of LBE
- 13 Assumptions
- 14 Existence ad uniqueness
- 15 Definition of LBE
- 16 Remarks
- 17 Empirical measure and current of N independent copies
- 18 Continuity equation
- 19 Large deviation principle
- 20 Microscopic model
- 21 The collision kernel
- 22 Large deviations (work in progress)
- 23 The rate functional
- 24 Entropy dissipation inequality
- 25 The Dirichlet integral and the the kinematic term
- 26 A gradient flow formulation
