A note on the entropy production of the radiative transfer equation

✍ Scribed by E. Gabetta; P.A. Markowich; A. Unterreiter

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 235 KB
• Volume: 12
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(99)00044-0

✦ Synopsis

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 e~(t), the entropy production I~(t), and the entropy production rate/'~(t) of the kinetic model. [~(t) has to be estimated in terms of I~(t). Then e~(t) is estimated in terms of I~(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. (~) 1999 Elsevier Science Ltd. All rights reserved.