Global existence for quadratic systems of reaction-diffusion

Advanced Nonlinear Studies

Volumn 7, Issue 3, 2007, Pages 491-511

  Desvillettes, Laurent ^a   Fellner, Klemens ^b   Pierre, Michel ^a   Vovelle, Julien ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b UNIVERSITY OF VIENNA   (Austria)

Author keywords

Entropy methods; Global existence; Lotka volterra systems; Reaction diffusion system; Renormalized solutions; Weak solutions

Indexed keywords

EID: 34547932449     PISSN: 15361365     EISSN: None     Source Type: Journal    
DOI: 10.1515/ans-2007-0309     Document Type: Article

References (16)

1. R. Alexandre, and C. Villani, On the Boltzmann equation for long-range interactions, Comm. Pure Appl. Math. 55, no. 1 (2002), 30-70.
2. R. Alexandre, and C. Villani, On the Landau approximation in plasma physics, Ann. Inst. H. Poincaré, Anal. Non Linéaire 21, no. 1 (2004), 61-95.
3. H. Amann, Global existence for semilinear parabolic problems, J. Reine Angew. Math. 360 (1985), 47-83.
4. P. Baras, and M. Pierre, Problèmes paraboliques semi-linéaires avec données mesures, Applicable Analysis 18 (1984), 111-149.
5. M. Bisi, L. Desvillettes, From Reactive Boltzmann Equations to Reaction-Diffusion Systems, To appear in J. Stat. Phys.
6. C. Cercignani, R. Illner, and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Springer, New-York, 1994.
7. L. Desvillettes, K. Fellner, Exponential Decay toward Equilibrium via Entropy Methods for Reaction-Diffusion Equations, J. Math. Anal. Appl. 319, no. 1 (2006), 157-176.
8. R. DiPerna, and P.-L. Lions, On the Cauchy problem for Boltzmann equations: global existence and weak stability, Ann. of Math. (2) 130, no.2 (1989), 321-366.
9. W.B. Fitzgibbon, S.L. Hollis, and J.J. Morgan, Stability and Lyapunov Functions for Reaction-Diffusion Systems, SIAM J. Math. Anal., Vol. 28, no. 3 (1997), 595-610.
10. O.A. Ladyzenskaya, V.A. Solonnikov, and N.N. Uralceva, Linear and Quasi-linear Equations of Parabolic Type, Trans. Math. Monographs, Vol. 23, Am. Math. Soc., Providence, 1968.
11. A. Leung, Systems of Nonlinear Partial Differential Equations, Kluwer Academic Publ. Boston, 1989.
12. 1 for reaction-diffusion systems, J. Evol. Equ. 3, no. 1 (2003), 153-168.
13. M. Pierre, D. Schmitt, Blowup in reaction-diffusion systems with dissipation of mass, SIAM Rev. 42 (2000), 93-106 (electronic).
14. F. Rothe, Global Solutions of Reaction-Diffusion Systems, Lecture Notes in Mathematics, Springer, Berlin, (1984).
15. p (0, T; B), Ann. Mat. Pura Appl, 146, no. 4 (1987), 65-96.
16. C. Villani, On the Cauchy problem for Landau equation: sequential stability, global existence, Adv. Differential Equations 1, no. 5 (1996) 793-816.