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The existence of an inertial manifold for a reaction-diffusion equation model of the chemostat is established.
[1]Chow, S.-N. and Lu, K., “Invariant manifolds for flows in Banach spaces”, J. Diff. Equ.74 (1988) 285–317.Google Scholar
[2]
[2]Foias, C., Sell, G. R. and Teman, R., “Inertial manifolds for nonlinear evolutionary equations”, J. Diff. Equ.73 (1988) 309–352.Google Scholar
[3]
[3]Hale, J. K., Asymptotic behavior of dissipative systems, Mathematical Survey and Monographs 25, Amer. Math. Soc, Providence, 1988.Google Scholar
[4]
[4]Kamaev, D. A., “Hopf's conjecture for a class of chemical kinetics equations”, J. Soviet Math.25 (1984) 836–849.Google Scholar
[5]
[5]Mallet-Paret, J. and Sell, G. R., “Inertial manifolds for reaction diffusion equations in higher space dimensions”, J. Amer. Math. Soc.1 (1988) 805–866.Google Scholar
[7]Smoller, J., Shock waves and reaction-diffusion equations, Springer-Verlag, New York, 1983.Google Scholar
[8]
[8]So, J. W.-H. and Waltman, P., “A nonlinear boundary value problem arising from competition in the chemostat”, Appl. Math. Comp.32 (1989) 169–183.CrossRefGoogle Scholar
[9]
[9]Teman, R., Infinite dimensional dynamical systems in mechanics and physics, Springer-Verlag, New York, 1988.Google Scholar