A generation theorem for kinetic equations with non-contractive boundary operators

Bertrand Lods

doi:10.1016/S1631-073X(02)02533-5

A generation theorem for kinetic equations with non-contractive boundary operators
[Un résultat de génération pour des équations cinétiques soumises à des conditions frontières non contractives]

Bertrand Lods ¹

¹ Département de mathématiques, Université de Franche-Comté, 16, route de Gray, 25030 Besancon, France

Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 655-660.

Abstract (VO)
Résumé

In this Note, we present some c₀-semigroup generation results in L_p-spaces for the advection operator submitted to non-contractive boundary conditions covering in particular the classical Maxwell-type boundary conditions.

Dans cette Note, on présente quelques résultats de génération de c₀-semigroupe dans les espaces L_p pour l'opérateur d'advection soumis à des conditions aux limites non contractives, couvrant par exemple les conditions frontières de type Maxwell.

Reçu le : 2002-04-04
Accepté le : 2002-07-23
Publié le : 2002-09-11

DOI : 10.1016/S1631-073X(02)02533-5

Affiliations des auteurs :

Bertrand Lods ¹

¹ Département de mathématiques, Université de Franche-Comté, 16, route de Gray, 25030 Besancon, France

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Bertrand Lods. A generation theorem for kinetic equations with non-contractive boundary operators. Comptes Rendus. Mathématique, Volume 335 (2002) no. 7, pp. 655-660. doi : 10.1016/S1631-073X(02)02533-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02533-5/

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Yan Guo; Xiongfeng Yang Existence and BV-regularity for neutron transport equation in nonconvex domain, SIAM Journal on Mathematical Analysis, Volume 48 (2016) no. 5, pp. 3467-3495 | DOI:10.1137/16m1059035 | Zbl:1362.35203
Nadjeh Redjel; Abdelkader Dehici Some compactness and interpolation results for linear Boltzmann equation, Journal of Function Spaces, Volume 2015 (2015), p. 8 (Id/No 370294) | DOI:10.1155/2015/370294 | Zbl:1323.47084
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Bertrand Lods On the spectrum of absorption operators with Maxwell boundary conditions arising in population dynamics and transport theory. A unified treatment, Transport Theory and Statistical Physics, Volume 37 (2008) no. 1, pp. 1-37 | DOI:10.1080/00411450802271684 | Zbl:1214.82136
Bertrand Lods; Mohammed Sbihi Stability of the essential spectrum for 2D-transport models with Maxwell boundary conditions, Mathematical Methods in the Applied Sciences, Volume 29 (2006) no. 5, pp. 499-523 | DOI:10.1002/mma.684 | Zbl:1092.35057
B. Lods Semigroup generation properties of streaming operators with noncontractive boundary conditions, Mathematical and Computer Modelling, Volume 42 (2005) no. 13, pp. 1441-1462 | DOI:10.1016/j.mcm.2004.12.007 | Zbl:1103.47033

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