## 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.

Original language | English (US) |
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Pages (from-to) | 111-116 |

Number of pages | 6 |

Journal | Applied Mathematics Letters |

Volume | 12 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1999 |

## Keywords

- Convex Sobolev inequality
- Entropy
- Entropy production
- Radiative transfer

## ASJC Scopus subject areas

- Applied Mathematics