Anderson, N.; Arthurs, A. M. Analytical bounding functions for diffusion problems with Michaelis- Menten kinetics. (English) Zbl 0554.92005 Bull. Math. Biol. 47, 145-153 (1985). Pointwise upper and lower bounds for the solution of a class of nonlinear diffusion problems with Michaelis-Menten kinetics are presented. Simple analytical bounding curves are obtained and for an illustrative case the calculated values bound the recent numerical solution of P. Hiltmann and P. Lory, ibid. 45, 661-664 (1983; Zbl 0512.92008). Cited in 2 ReviewsCited in 25 Documents MSC: 92Cxx Physiological, cellular and medical topics 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 35K20 Initial-boundary value problems for second-order parabolic equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:nonlinear diffusion; Michaelis-Menten kinetics; analytical bounding curves Citations:Zbl 0512.92008 PDFBibTeX XMLCite \textit{N. Anderson} and \textit{A. M. Arthurs}, Bull. Math. Biol. 47, 145--153 (1985; Zbl 0554.92005) Full Text: DOI References: [1] Amann, H. 1971. ”On the Existence of Positive Solutions of Nonlinear Elliptic Boundary Value Problems.”Indiana Univ. Math. J. 21, 125–146. · Zbl 0219.35037 · doi:10.1512/iumj.1972.21.21012 [2] Anderson, N. and A. M. Arthurs. 1980. ”Complementary Variational Principles for Diffusion Problems with Michaelis-Menten Kinetics.”Bull. math. Biol. 42, 131–135. · Zbl 0423.92040 · doi:10.1007/BF02462371 [3] Ghim, Y. S. and H. N. Chang. 1983. ”Diffusional Falsification of Kinetic Constants on Lineweaver-Burk Plots.”J. theor. Biol. 105, 91–102. · doi:10.1016/0022-5193(83)90426-5 [4] Hiltmann, P. and P. Lory. 1983. ”On Oxygen Diffusion in a Spherical Cell with Michaelis-Menten Oxygen Uptake Kinetics.”Bull. math. Biol. 45, 661–664. · Zbl 0512.92008 · doi:10.1007/BF02460043 [5] Lin, S. H. 1976. ”Oxygen Diffusion in a Spherical Cell with Nonlinear Oxygen Uptake Kinetics.”J. theor. Biol. 60, 449–457. · doi:10.1016/0022-5193(76)90071-0 [6] McElwain, D. L. S. 1978. ”A Re-examination of Oxygen Diffusion in a Spherical Cell with Michaelis-Menten Oxygen Uptake Kinetics.”J. theor. Biol. 71, 255–263. · doi:10.1016/0022-5193(78)90270-9 [7] Villadsen, J. and M. L. Michelsen. 1978.Solution of Differetial Equation Models by Polynomial Approximation. Englewood Cliffs, New Jersey: Prentice-Hall. · Zbl 0464.34001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.