Quasi-steady-state approximation for a reaction-diffusion system with fast intermediate

Journal of Mathematical Analysis and Applications

Volumn 368, Issue 1, 2010, Pages 120-132

  Bothe, Dieter ^a   Pierre, Michel ^b  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Blow up; Bodenstein approximation; Pseudo steady state approximation; QSSA; Reaction diffusion system; Weak global solution

Indexed keywords

EID: 77951208201     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2010.02.044     Document Type: Article

References (29)

1. Amann H. Global existence for semilinear parabolic problems. J. Reine Angew. Math. 1985, 360:47-83.
2. Baras P. Non-unicité des solutions d'une équation d'évolution non-linéaire. Ann. Fac. Sci. Toulouse Math. 1983, 5:287-302.
3. Baras P., Pierre M. Problèmes paraboliques semi-linéaires avec données mesures. Appl. Anal. 1984, 18:111-149.
4. Ph. Bénilan, M.G. Crandall, A. Pazy, Nonlinear Evolution Equations in Banach Spaces, preprint book.
5. Bisi M., Conforto F., Desvillettes L. Quasi-steady-state approximation for reaction-diffusion equations. Bull. Inst. Math. Acad. Sin. (N.S.) 2007, 2:823-850.
6. Bothe D. Flow invariance for perturbed nonlinear evolution equations. Abstr. Appl. Anal. 1996, 1:417-433.
7. Bothe D. The instantaneous limit of a reaction-diffusion system. Lect. Notes Pure Appl. Math. 2000, vol. 215:215-224. Marcel Dekker. G. Lumer, L. Weis (Eds.).
8. Bothe D. Instantaneous limits of reversible chemical reactions in presence of macroscopic convection. J. Differential Equations 2003, 193:27-48.
9. Bothe D., Hilhorst D. A reaction-diffusion system with fast reversible reaction. J. Math. Anal. Appl. 2003, 286:125-135.
10. D. Bothe, M. Pierre, The instantaneous limit for reaction-diffusion systems with a fast irreversible reaction, Discrete Contin. Dyn. Syst. Ser. S, in press.
11. Desvillettes L., Fellner K., Pierre M., Vovelle J. About global existence for quadratic systems of reaction-diffusion. Adv. Nonlinear Stud. 2007, 7:491-511.
12. Erdi P., Toth J. Mathematical Models of Chemical Reactions 1989, Manchester Univ. Press.
13. Espenson J.H. Chemical Kinetics and Reaction Mechanisms 1995, McGraw-Hill. 2nd ed.
14. Fitzgibbon W.B., Hollis S.L., Morgan J.J. Stability and Lyapunov functions for reaction-diffusion systems. SIAM J. Math. Anal. 1997, 28:595-610.
15. Gorban A.N., Karlin I.V. Method of invariant manifold for chemical kinetics. Chem. Eng. Sci. 2003, 58:4751-4768.
16. Goudon Th., Vasseur A. Regularity analysis for systems of reaction-diffusion equations. Ann. Sci. Ecole Norm. Sup. 2010, 43:117-141.
17. Haraux A., Weissler F.B. Non-uniqueness for a semilinear initial value problem. Indiana Univ. Math. J. 1982, 31:167-189.
18. Henry D. Geometric Theory of Semilinear Parabolic Equations. Lecture Notes in Math. 1981, vol. 840. Springer, Berlin.
19. Hollis S.L., Martin R.H., Pierre M. Global existence and boundedness in reaction-diffusion systems. SIAM J. Math. Anal. 1987, 18:744-761.
20. Kalachev L.V., Kaper H.G., Kaper T.J., Popović N., Zagaris A. Reduction for Michaelis-Menten-Henri kinetics in the presence of diffusion. Electron. J. Differ. Equ. Conf. 2007, 16:155-184.
21. Ladyzenskaya O.A., Solonnikov V.A., Ural'ceva N.N. Linear and Quasi-Linear Equations of Parabolic Type. Transl. Math. Monogr. 1968, vol. 23. Amer. Math. Soc., Providence.
22. Martin R.H., Pierre M. Nonlinear reaction-diffusion systems. Math. Sci. Eng. 1991, vol. 185:363-398. Academic Press, New York. W.F. Ames, C. Rogers (Eds.).
23. Morgan J. Global existence for semilinear parabolic systems. SIAM J. Math. Anal. 1989, 20:1128-1144.
24. M. Pierre, Global existence in reaction-diffusion systems with control of mass: a survey, Milan J. Math., in press.
25. Pierre M. Weak solutions and supersolutions in L1 for reaction-diffusion systems. J. Evol. Equ. 2003, 3:153-168.
26. Pierre M., Schmitt D. Blow up in reaction-diffusion systems with dissipation of mass. SIAM J. Math. Anal. 1997, 28:259-269.
27. Pierre M., Schmitt D. Blowup in reaction-diffusion systems with dissipation of mass. SIAM Rev. 2000, 42:93-106. (electronic).
28. Rothe F. Global Solutions of Reaction-Diffusion Systems. Lecture Notes in Math. 1984, vol. 1072. Springer, Berlin.
29. Segel L.A., Slemrod M. The quasi-steady-state assumption: a case study in perturbation. SIAM Rev. 1989, 31:446-477.