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 $D\left ( c \right ) = \exp c$.
L. E. Shampine, Quart. Appl. Math. 30, 441–452 (1973)
L. F. Shampine, Quart. Appl. Math. 34, 429–431 (1976)
- 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 100516, DOI https://doi.org/10.1007/bf02476456
A. M. Arthurs, Complementary variational principles, Oxford, 1970
- B. Noble and M. J. Sewell, On dual extremum principles in applied mathematics, J. Inst. Math. Appl. 9 (1972), 123–193. MR 307012
- 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 416246
L. E. Shampine, Quart. Appl. Math. 30, 441–452 (1973)
L. F. Shampine, Quart. Appl. Math. 34, 429–431 (1976)
R. I. Macey, Bull. Math. Biophys. 21, 19–32 (1959)
A. M. Arthurs, Complementary variational principles, Oxford, 1970
B. Noble and M. J. Sewell, J. Inst. Math. Appl. 9, 123–193 (1972)
N. Anderson and A. M. Arthurs, J. Inst. Math. Appl. 13, 153–159 (1974)
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Article copyright:
© Copyright 1977
American Mathematical Society
