Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Dual extremum principles for a nonlinear diffusion problem

Authors: N. Anderson and A. M. Arthurs
Journal: Quart. Appl. Math. 35 (1977), 188-190
MSC: Primary 76.49
DOI: https://doi.org/10.1090/qam/475282
MathSciNet review: 475282
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Abstract: Maximum and minimum principles for a nonlinear boundary value problem in diffusion with concentration-dependent coefficient $ D\left( c \right)$ are derived in a unified manner from the theory of dual extremum principles. The results are illustrated by a calculation in the case $ D\left( c \right) = \exp c$.

References [Enhancements On Off] (What's this?)

  • [1] L. E. Shampine, Quart. Appl. Math. 30, 441-452 (1973)
  • [2] L. F. Shampine, Quart. Appl. Math. 34, 429-431 (1976)
  • [3] Robert I. Macey, A quasi-steady-state approximation method for diffusion problems: I. Concentration dependent diffusion coefficients, Bull. Math. Biophys 21 (1959), 19–32. MR 0100516
  • [4] A. M. Arthurs, Complementary variational principles, Oxford, 1970
  • [5] B. Noble and M. J. Sewell, On dual extremum principles in applied mathematics, J. Inst. Math. Appl. 9 (1972), 123–193. MR 0307012
  • [6] N. Anderson and A. M. Arthurs, Complementary variational principles for a class of non-linear diffusion equations, J. Inst. Math. Appl. 13 (1974), 153–159. MR 0416246

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DOI: https://doi.org/10.1090/qam/475282
Article copyright: © Copyright 1977 American Mathematical Society

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