A note on the entropy production of the radiative transfer equation Original Research Article

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.