General entropy equations for structured population models and scattering;Un principe général d'entropie pour les modèles de population structurés et les équations de scattering

Comptes Rendus Mathematique

Volumn 338, Issue 9, 2004, Pages 697-702

  Michel, Philippe ^a,b   Mischler, Stéphane ^a   Perthame, Benoît ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1842843699     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2004.03.006     Document Type: Article

References (21)

1. Adimy M. Pujo-Menjouet L. Asymptotic behavior of a singular transport equation modelling cell division DCDS(B) 3 3 2003 439-456
2. Arino O. A survey of structured cell population dynamics Acta Biotheor. 43 1995 3-25
3. Basse B. Bagulay B.C. Marshall E.S. Joseph W.R. van Brunt B. Wake G. Wall D.J.N. A mathematical model for analysis of the cell cycle in cell lines derived from human tumors J. Math. Biol. 2003
4. Chalub F. Markowich P. Perthame B. Schmeiser C. Kinetic models for chemotaxis and their drift-diffusion limits, Monat. Math., in press
5. Chiorino G. Metz J.A.J. Tomasoni D. Ubezio P. Desynchronization rate in cell populations: mathematical modeling and experimental data J. Theor. Biol. 208 2001 185-199
6. Càceres M.J. Carillo J.A. Goudon T. Equilibrium rate for the linear inhomogeneous relaxation time Boltzmann equation for charged particles Comm. Partial Differential Equations 28 1-2 2003 969-989
7. Dautray R. Lions J.-L. Mathematical Analysis and Numerical Methods for Sciences and Technology 1990 Springer
8. Degond P. Goudon T. Poupaud F. Diffusion approximation for non homogeneous and non microreversible processes Indiana Univ. Math. J. 49 2000 1175-1198
9. Desvillettes L. Villani C. Entropic methods for the study of the longtime behavior of kinetic equations The Sixteenth International Conference on Transport Theory, Part I (Atlanta, GA, 1999) Transport Theory Statist. Phys. 30 2-3 2001 155-168
10. Fournier N. Mischler S. Trend to equilibrium for discrete coagulation equations with strong fragmentation and without balance condition, Preprint, 2003
11. Huyer W. On periodic cohort solutions of a size-structured population model J. Math. Biol. 35 8 1997 908-934
12. Lebowitz J.L. Rubinow S.I. A theory for the age and generation time distribution of a microbial population J. Math. Biol. 1 1977 17-36
13. Lods B. Toscani G. The dissipative linear Boltzmann equation for hard spheres, Appl. Math. Lett., in press
14. Mellet A. Diffusion limit of a non linear kinetic model without the detailed balance principle Monat. Math. 134 2002 305-329
15. Metz J.A.J. Diekmann O. The Dynamics of Physiologically Structured Populations Lecture Notes in Biomath. vol. 68 1986 Springer-Verlag
16. Michel P. Mischler S. Perthame B. The entropy structure of models of structured population dynamics, in preparation
17. Mischler S. Perthame B. Ryzhik L. Stability in a nonlinear population maturation model Math. Models Meth. Appl. Sci. 12 12 2002 1751-1772
18. Perthame B. Ryzhik, L. Exponential decay for the fragmentation or cell-division equation, Preprint DMA, 2003
19. Rotenberg M. Transport theory for growing cell populations J. Theor. Biol. 103 1983 181-199
20. Villani C. Topics in Optimal Transportation Graduate Stud. Math. vol. 58 2003 American Mathematical Society Providence, RI
21. Villani C. A review of mathematical topics in collisional kinetic theory, in: S. Friedlander, D. Serre (Eds.), Handbook of Mathematical Fluid Dynamics Tome I, Chapter 2