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
e
ϕ
(
t), the entropy production
I
ϕ
(
t), and the entropy production rate
I
ϕ
(
t) of the kinetic model.
I
ϕ
(
t) has to be estimated in terms of
I
ϕ
(
t). Then
e
ϕ
(
t) is estimated in terms of
I
ϕ
(
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.