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]
Lods, Bertrand1
1 Département de mathématiques, Université de Franche-Comté, 16, route de Gray, 25030 Besancon, France
Comptes Rendus. Mathématique, Tome 335 (2002) no. 7, pp. 655-660.

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

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02533-5
Lods, Bertrand 1

1 Département de mathématiques, Université de Franche-Comté, 16, route de Gray, 25030 Besancon, France 
@article{CRMATH_2002__335_7_655_0,
     author = {Lods, Bertrand},
     title = {A generation theorem for kinetic equations with non-contractive boundary operators},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {655--660},
     publisher = {Elsevier},
     volume = {335},
     number = {7},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02533-5},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02533-5/}
}
TY  - JOUR
AU  - Lods, Bertrand
TI  - A generation theorem for kinetic equations with non-contractive boundary operators
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 655
EP  - 660
VL  - 335
IS  - 7
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02533-5/
DO  - 10.1016/S1631-073X(02)02533-5
LA  - en
ID  - CRMATH_2002__335_7_655_0
ER  - 
%0 Journal Article
%A Lods, Bertrand
%T A generation theorem for kinetic equations with non-contractive boundary operators
%J Comptes Rendus. Mathématique
%D 2002
%P 655-660
%V 335
%N 7
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02533-5/
%R 10.1016/S1631-073X(02)02533-5
%G en
%F CRMATH_2002__335_7_655_0
Lods, Bertrand. A generation theorem for kinetic equations with non-contractive boundary operators. Comptes Rendus. Mathématique, Tome 335 (2002) no. 7, pp. 655-660. doi : 10.1016/S1631-073X(02)02533-5. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02533-5/

[1] Batty, J.K.; Robinson, D.W. Positive one parameter semigroups on ordered spaces, Acta Appl. Math., Volume 1 (1984), pp. 221-296

[2] Boulanouar, M. Le transport neutronique avec des conditions aux limites générales, C. R. Acad. Sci. Paris, Série I, Volume 329 (1999), pp. 121-124

[3] Busoni, G.; Frosali, G. Streaming operators and semigroups, Meccanica, Volume 14 (1979), pp. 119-128

[4] Cercignani, C. The Boltzmann Equation and its Applications, Springer, 1987

[5] Cercignani, C.; Illner, R.; Pulvirenti, M. The Mathematical Theory of Dilute Gases, Springer-Verlag, 1994

[6] Greenberg, W.; Van der Mee, C.; Protopopescu, V. Boundary Value Problems in Abstract Kinetic Theory, Birkhäuser, Basel, 1987

[7] Latrach, K.; Mokhtar-Kharroubi, M. Spectral analysis and generation results for streaming operators with multipliying boundary conditions, Positivity, Volume 3 (1999), pp. 273-296

[8] B. Lods, Théorie spectrale des équations cinétiques, Thèse, à paraı̂tre

[9] Lods, B.; Mokhtar-Kharroubi, M. On the theory of a growing cell population with zero minimum cycle length, J. Math. Anal. Appl., Volume 266 (2001), pp. 70-99

[10] Van Der Mee, C. Time dependent kinetic equations with collision terms relatively bounded with respect to the collision frequency, Transport Theory Statist. Phys., Volume 30 (2001), pp. 63-90

[11] Webb, G.F. A model of prolifetaring cell population with inherited cycle length, J. Math. Biol., Volume 23 (1986), pp. 269-282

Cité par Sources :