Free Access
Issue
ESAIM: M2AN
Volume 43, Number 1, January-February 2009
Page(s) 151 - 172
DOI https://doi.org/10.1051/m2an:2008045
Published online 05 December 2008
  1. A. Arnold, J.A. Carrillo, L. Desvillettes, J. Dolbeault, A. Jungel, C. Lederman, P.A. Markowich, G. Toscani and C. Villani, Entropies and equilibria of many-particle systems: An essay on recent research. Monat. Mathematik 142 (2004) 35–43. [CrossRef] [Google Scholar]
  2. M. Bisi and L. Desvillettes, From reactive Boltzmann equations to reaction-diffusion systems. J. Stat. Phys. 124 (2006) 881–912. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Bisi and G. Spiga, Diatomic gas diffusing in a background medium: kinetic approach and reaction-diffusion equations. Commun. Math. Sci. 4 (2006) 779–798. [MathSciNet] [Google Scholar]
  4. M. Bisi and G. Spiga, Dissociation and recombination of a diatomic gas in a background medium. Proceedings of 25th International Symposium on Rarefied Gas Dynamics (to appear). [Google Scholar]
  5. M. Cáceres, J. Carrillo and G. Toscani, Long-time behavior for a nonlinear fourth order parabolic equation. Trans. Amer. Math. Soc. 357 (2005) 1161–1175. [CrossRef] [MathSciNet] [Google Scholar]
  6. J.A. Carrillo and G. Toscani, Asymptotic L1-decay of solutions of the porous medium equation to self-similarity. Indiana University Math. J. 49 (2000) 113–142. [Google Scholar]
  7. M. Del Pino and J. Dolbeault, Best constants for Gagliardo-Nirenberg inequalities and applications to nonlinear diffusions. J. Math. Pures Appl. 81 (2002) 847–875. [CrossRef] [MathSciNet] [Google Scholar]
  8. L. Desvillettes, About entropy methods for reaction-diffusion equations. Rivista Matematica dell'Università di Parma 7 (2007) 81–123. [Google Scholar]
  9. L. Desvillettes and K. Fellner, Exponential decay toward equilibrium via entropy methods for reaction-diffusion equations. J. Math. Anal. Appl. 319 (2006) 157–176. [CrossRef] [MathSciNet] [Google Scholar]
  10. L. Desvillettes and K. Fellner, Entropy methods for reaction-diffusion systems: Degenerate diffusion. Discrete Contin. Dyn. Syst. Supplement (2007) 304–312. [Google Scholar]
  11. L. Desvillettes and K. Fellner, Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds. Revista Mat. Iberoamericana (to appear). [Google Scholar]
  12. L. Desvillettes and C. Villani, On the spatially homogeneous Landau equation for hard potentials. II. H-theorem and applications. Comm. Partial Differ. Equ. 25 (2000) 261–298. [CrossRef] [Google Scholar]
  13. V. Giovangigli, Multicomponent Flow Modeling. Birkhäuser, Boston (1999). [Google Scholar]
  14. M. Groppi, A. Rossani and G. Spiga, Kinetic theory of a diatomic gas with reactions of dissociation and recombination through a transition state. J. Phys. A 33 (2000) 8819–8833. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Kirane, On stabilization of solutions of the system of parabolic differential equations describing the kinetics of an auto-catalytic reversible chemical reaction. Bull. Institute Math. Academia Sinica 18 (1990) 369–377. [Google Scholar]
  16. O.A. Ladyzenskaya, V.A. Solonnikov and N.N. Uralceva, Linear and Quasi-linear Equations of Parabolic Type, Trans. Math. Monographs 23. American Mathematical Society, Providence (1968). [Google Scholar]
  17. K. Masuda, On the global existence and asymptotic behavior of solution of reaction-diffusion equations. Hokkaido Math. J. 12 (1983) 360–370. [MathSciNet] [Google Scholar]
  18. J.A. McLennan, Boltzmann equation for a dissociating gas. J. Stat. Phys. 57 (1989) 887–905. [CrossRef] [Google Scholar]
  19. Y. Sone, Kinetic Theory and Fluid Dynamics. Birkhäuser, Boston (2002). [Google Scholar]
  20. G. Toscani and C. Villani, Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation. Comm. Math. Phys. 203 (1999) 667–706. [CrossRef] [MathSciNet] [Google Scholar]
  21. Y. Yoshizawa, Wave structures of a chemically reacting gas by the kinetic theory of gases, in Rarefied Gas Dynamics, J.L. Potter Ed., A.I.A.A., New York (1977) 501–517. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you