Entropy Method for Hypocoercive BGK and Fokker-Planck Equations

Entropy Method for Hypocoercive BGK and Fokker-Planck Equations

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Proof of Proposition 2 - modified entropy method

11 of 14

11 of 14

Proof of Proposition 2 - modified entropy method

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Classroom Contents

Entropy Method for Hypocoercive BGK and Fokker-Planck Equations

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  1. 1 Intro
  2. 2 degenerate Fokker-Planck equations with linear drift
  3. 3 degenerate prototype with w = 1
  4. 4 coefficients C. Din Fokker-Planck equation
  5. 5 review of entropy method
  6. 6 admissible relative entropies (for entropy method) for probability densities
  7. 7 Step 1: exponent decay of entropy dissipation for D=const
  8. 8 Step 2. exponential decay of relative entropy for Deconst Theorem 4
  9. 9 problem of entropy decay (cp. standard entropy method)
  10. 10 Step 1: exponential decay of auxiliary functional S.
  11. 11 Proof of Proposition 2 - modified entropy method
  12. 12 (parabolic) regularization of semigroup e
  13. 13 local vs. global decay rate in non-symmetric FP equations decay of logarithmic entropy for the non-symmetric FP equation
  14. 14 Why does the hypocoercive method work?

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