Exponential convergence to equilibrium via Lyapounov functionals for reaction-diffusion equations arising from non reversible chemical kinetics

 Access to full text

 Full (PDF)

1. [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. Zbl1063.35109MR2065020
2. [2] M. Bisi and L. Desvillettes, From reactive Boltzmann equations to reaction-diffusion systems. J. Stat. Phys. 124 (2006) 881–912. Zbl1134.82323MR2264629
3. [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. Zbl1120.82011MR2264820
4. [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). Zbl1120.82011MR2264820
5. [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. Zbl1077.35028MR2110436
6. [6] J.A. Carrillo and G. Toscani, Asymptotic $L^1$-decay of solutions of the porous medium equation to self-similarity. Indiana University Math. J. 49 (2000) 113–142. Zbl0963.35098MR1777035
7. [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. Zbl1112.35310MR1940370
8. [8] L. Desvillettes, About entropy methods for reaction-diffusion equations. Rivista Matematica dell’Università di Parma 7 (2007) 81–123. Zbl1171.35409MR2375204
9. [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. Zbl1096.35018MR2217853
10. [10] L. Desvillettes and K. Fellner, Entropy methods for reaction-diffusion systems: Degenerate diffusion. Discrete Contin. Dyn. Syst. Supplement (2007) 304–312. Zbl1163.35322MR2409225
11. [11] L. Desvillettes and K. Fellner, Entropy methods for reaction-diffusion equations: slowly growing a-priori bounds. Revista Mat. Iberoamericana (to appear). Zbl1171.35330MR2459198
12. [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. Zbl0951.35130MR1737548
13. [13] V. Giovangigli, Multicomponent Flow Modeling. Birkh$\ddot{\mathrm{a}}$user, Boston (1999). Zbl0956.76003MR1713516
14. [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. Zbl0970.82041MR1801471
15. [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. Zbl0731.35056MR1104954
16. [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). Zbl0174.15403
17. [17] K. Masuda, On the global existence and asymptotic behavior of solution of reaction-diffusion equations. Hokkaido Math. J. 12 (1983) 360–370. Zbl0529.35037MR719974
18. [18] J.A. McLennan, Boltzmann equation for a dissociating gas. J. Stat. Phys. 57 (1989) 887–905. 
19. [19] Y. Sone, Kinetic Theory and Fluid Dynamics. Birkh$\ddot{\mathrm{a}}$user, Boston (2002). Zbl1021.76002MR1919070
20. [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. Zbl0944.35066MR1700142
21. [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.