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Boundedness for a system of reaction-diffusion equations 1

Part of:Parabolic equations and systems

Published online by Cambridge University Press:  26 February 2010

S. S. Okoya
S. S. Okoya
Affiliation:
Department of Mathematics, Obafemi Awolowo University, lle, Ife, Nigeria.
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Abstract

In this paper, we consider an extended model of a coupled nonlinear reaction-diffusion equations with Neumann-Neumann boundary conditions. We obtain upper linear growth bound for one of the components. We also find the corresponding bound for the case of Dirichlet-Dirichlet boundary conditions.

MSC classification

Secondary:35K57: Reaction-diffusion equations

Information

Type
Research Article
Information
Mathematika , Volume 41 , Issue 2 , December 1994, pp. 293 - 300
Copyright
Copyright © University College London 1994

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References

1.Avrin, J. D.. Qualitative theory of the Cauchy problem for a one-step reaction model on bounded domains. SIAM Jl. Math. Analysis, 22 (1991), 379–391.CrossRefGoogle Scholar
2.Avrin, J. D. and Kirane, M.. Temperature growth and temperature bounds in special cases of combustion models. Applicable Analysis, 50 (1993), 131–144.CrossRefGoogle Scholar
3.Bebernes, J. and Eberly, D.. Mathematical Problems from Combustion, Applied Math. Sci. Series, 83 (Springer-Verlag, New York, 1989).CrossRefGoogle Scholar
4.Bebernes, J. and Lacey, A.. Finite time blow up for semilinear reaction-diffusion systems. Journal of Differential Equations, 95 (1992), 105–129.CrossRefGoogle Scholar
5.Boddington, T., Feng, C. and Gray, P.. Thermal explosions, criticality and the disappearance of criticality in systems with distributed temperatures 1. Arbitrary Biot number and general reaction rate laws. Proc. R. Soc. London, A390 (1983), 247–264.Google Scholar
6.Buckmaster, J. and Ludford, G. S. S.. Theory of Laminar Flames (Cambridge University Press, 1982).CrossRefGoogle Scholar
7.Dainton, F. S.. Chain Reactions: An Introduction (Wiley Press, New York, 1966).Google Scholar
8.Groot, S. R. De and Mazur, P.. Non-equilibrium Thermodynamics (North-Holland Publishing Company, Amsterdam, 1962).Google Scholar
9.Friedman, A.. Generalized functions and partial differential equations (Prentice-Hall, Englewood Cliffs, N.J., 1963).CrossRefGoogle Scholar
10.Hollis, S. L., Martin, R. H. and Pierre, M.. Global existence and boundedness in reaction-diffusion systems. SIAM Journal of Math. Analysis, 18 (1987), 744–761.CrossRefGoogle Scholar
11.Kahane, C. S.. On the asymptotic behaviour of solutions of parabolic equations. Czechoslovak Mathematical Journal, 33 (1983), 262–285.CrossRefGoogle Scholar
12.Kirane, M.. Global bounds and asymptotics for a system of reaction-diffusion equations. Journal of Mathematical Analysis and Applications, 138 (1989), 328–342.CrossRefGoogle Scholar
13.Kirane, M.. Unbounded solutions for the Brusselator. ICTP Preprint IC/92/30 (1992).Google Scholar
14.Okoya, S. S.. A mathematical model for explosions with chain branching and chain breaking kinetics. Ph.D. thesis, Obafemi Awolowo University, Nigeria (1989).Google Scholar
15.Protter, M. H. and Weinberger, H. F.. Maximum Principles in Differential Equations (Prentice-Hall, Englewood Cliffs, N.J., 1967).Google Scholar
16.Williams, F.. Combustion Theory (Second Edition, Addison-Wesley, 1985).Google Scholar