A note on the entropy production of the radiative transfer equation

E. Gabetta*, Peter Markowich, A. Unterreiter

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

In recent years, the entropy approach to the asymptotic (large-time) analysis of homogeneous kinetic models has led to remarkable new proofs of convex-type (e.g., logarithmic) Sobolev inequalities. The crucial point of this method lies in computing the entropy eφ(t), the entropy production Iφ(t), and the entropy production rate Iφ(t) of the kinetic model. Iφ(t) has to be estimated in terms of Iφ(t). Then eφ(t) is estimated in terms of Iφ(t). We apply this approach to the (explicitly solvable) homogeneous radiative transfer equation obtaining a Jensen-type inequality involving a convex function as corresponding "Sobolev inequality". All the computations are highly transparent and serve to highlight and ultimately clarify the approach.

Original languageEnglish (US)
Pages (from-to)111-116
Number of pages6
JournalApplied Mathematics Letters
Volume12
Issue number4
DOIs
StatePublished - Jan 1 1999

Keywords

  • Convex Sobolev inequality
  • Entropy
  • Entropy production
  • Radiative transfer

ASJC Scopus subject areas

  • Applied Mathematics

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