A priori bounds and global existence of solutions of the steady-state Sel'kov model

Royal Society of Edinburgh - Proceedings A

Volumn 130, Issue 3, 2000, Pages 507-516

  Davidson, F A ^a   Rynne, B P ^b  

^a UNIVERSITY OF DUNDEE   (United Kingdom)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044517800     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500000275     Document Type: Article

References (18)

1. R. A. Adams. Sobolev spaces (Academic, 1975).
2. S. Agmon, A. Douglis and L. Nirenberg. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I. Commun. Pure Appl. Math. 12 (1959), 623-727.
3. K. J. Brown and F. A. Davidson. Global bifurcation in the Brusselator system. Nonlinear Analysis Theory Meth. Applic. 24 (1995), 1713-1725.
4. J. Cameron. Spectral collocation and path-following methods for reaction-diffusion equations in one and two space dimensions. PhD thesis, Heriot-Watt University, Edinburgh (1994).
5. M. Crandall and P. H. Rabinowitz. Bifurcation from simple eigenvalues. J. Funct. Analysis 8 (1971), 321-340.
6. E. N. Dancer. On the structure of solutions of non-linear eigenvalue problems. Indiana Univ. Math. J. 23 (1974), 1069-1076.
7. D. E. Edmunds and W. D. Evans. Spectral theory and differential operators (Oxford University Press, 1990).
8. J. C. Eilbeck. Pattern formation and pattern selection in reaction diffusion systems. In Theoretical biology: epigenetic and evolutionary order (ed. B. Goodwin and P. T. Saunders), pp. 31-41 (Edinburgh University Press, 1989).
9. J. C. Eilbeck and J. E. Furter. Analysis of bifurcations in reaction-diffusion systems with no flux boundary conditions - the Selkov model. Proc. R. Soc. Edinb. A 125 (1995), 413-438.
10. A. Hunding and P. G. Sorensen. Size adaptation of Turing prepatterns. J. Math. Biol. 26 (1988), 27-39.
11. J. Lopez-Gomez, J. C. Eilbeck, M. Molina and K. N. Duncan. Structure of solution manifolds in a strongly coupled elliptic system. IMA J. Numerical Analysis 12 (1992), 405-428.
12. J. D. Murray. Mathematical biology (Springer, 1989).
13. P. H. Rabinowitz. Nonlinear Sturm-Liouville problems for second-order ordinary differential equations. Commun. Pure Appl. Math. 23 (1970), 939-961.
14. P. H. Rabinowitz. Some global results for nonlinear eigenvalue problems. J. Funct. Analysis 7 (1971), 487-513.
15. S. D. Scott and P. Gray. Chemical reactions in isothermal systems: oscillations and instabilities. In Nonlinear phenomena and chaos (ed. S. Sarkar), pp. 70-96 (Bristol: Adam Hilger, 1986).
16. E. E. Sel'kov. Self-oscillations in glycolysis. Eur. J. Biochem. 4 (1968), 79-86.
17. K. Uhlenbeck. Generic properties of eigenfunctions. Am. J. Math. 98 (1976), 1059-1078.
18. E. Zeidler. Nonlinear functional analysis and its applications, vol. I (Springer, 1986).