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Online ISSN 1552-4485; Print ISSN 0033-569X
Variational solutions for two nonlinear boundary-value problems for diffusion with concentration-dependent coefficients
Author:
R. I. Reeves
Journal:
Quart. Appl. Math. 33 (1975), 291-295
MSC:
Primary 80.49
DOI:
https://doi.org/10.1090/qam/449208
MathSciNet review:
449208
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Abstract | References | Similar Articles | Additional Information
Abstract: The theory of complementary variational principles is used to obtain variational solutions for two nonlinear boundary-value problems which arise in the theory of diffusion with concentration-dependent coefficients.
- C. F. Lee, On the solution of some diffusion equations with concentration-dependent diffusion coefficients, J. Inst. Math. Appl. 8 (1971), 251–259. MR 301946
- L. F. Shampine, Concentration-dependent diffusion, Quart. Appl. Math. 30 (1972/73), 441–452. MR 413785, DOI https://doi.org/10.1090/S0033-569X-1973-0413785-8
- L. F. Shampine, Concentration-dependent diffusion, Quart. Appl. Math. 30 (1972/73), 441–452. MR 413785, DOI https://doi.org/10.1090/S0033-569X-1973-0413785-8
- J. Crank, The mathematics of diffusion, Oxford, at the Clarendon Press, 1956. MR 0082827
- Arnold Magowan Arthurs, Complementary variational principles, 2nd ed., The Clarendon Press, Oxford University Press, New York, 1980. Oxford Mathematical Monographs. MR 594935
- 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
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Article copyright:
© Copyright 1975
American Mathematical Society