Abstract
The theory of complementary variational principles is used to obtain maximum and minimum principles for diffusion problems with Michaelis-Menten kinetics. In an illustrative calculation we obtain an extremely accurate variational solution in good agreement with the numerical solution of McElwain (1978).
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Literature
Anderson, N. and A. M. Arthurs. 1975. “Complementary Variational Principles for a Class of Diffusion-Kinetics Boundary Value Problems.”ZAMM,55, 192–193.
Arthurs, A. M. 1970.Complementary Variational Principles. Oxford: Clarendon Press.
— 1973. “Dual Extremum Principles and Error Bounds for a Class of Boundary Value Problems.”J. Math. Analysis Applic,41, 781–795.
Hooke, R. and T. A. Jeeves. 1961. “Direct Search Solution of Numerical and Statistical Problems.”J. Ass. Comput. Mach.,8, 212–229.
Lin, S. H. 1976. “Oxygen Diffusion in a Spherical Cell with Nonlinear Oxygen Uptake Kinetics.”J. Theor. Biol.,60, 449.
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.
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Anderson, N., Arthurs, A.M. Complementary variational principles for diffusion problems with Michaelis-Menten kinetics. Bltn Mathcal Biology 42, 131–135 (1980). https://doi.org/10.1007/BF02462371
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DOI: https://doi.org/10.1007/BF02462371