Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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: 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.

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

  • [1] C. F. Lee, On the solution of some diffusion equations with concentration-dependent diffusion coefficients, J. Inst. Math. Applics. 8, 251-259 (1971) MR 0301946
  • [2] L. F. Shampine, Concentration-dependent diffusion, Quart. Appl. Math. 30, 441-452 (1973) MR 0413785
  • [3] L. F. Shampine, Some singular concentration dependent diffusion problems, Zeit. Ange. Math. Mech. 53, 421-422 (1973) MR 0413785
  • [4] J. Crank, The mathematics of diffusion, Oxford University Press, London, 1956, Chapter 9 MR 0082827
  • [5] A. M. Arthurs, Complementary variational principles, Clarendon Press, Oxford, 1970 MR 594935
  • [6] N. Anderson and A. M. Arthurs, Complementary variational principles for a class of nonlinear diffusion equations, J. Inst. Math. Applic. 13, 153-159 (1974) MR 0416246

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DOI: https://doi.org/10.1090/qam/449208
Article copyright: © Copyright 1975 American Mathematical Society

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