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Separation of variables in the diffusion equation. II

Abstract

The covariant and symmetry properties of the linear diffusion equation having a scalar matrix of variable diffusion coefficients are studied. By means of differential symmetry operators of order no higher than two, a complete separation of variables is effected for the stationary and nonstationary cases.

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Literature cited

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    N. B. Sukhomlin, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 11, 46 (1976).

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    V. D. Egerev, Diffusion Kinetics in Inhomogeneous Media [in Russian], Nauka, Moscow (1970).

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    N. B. Sukhomlin, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 1, 146 (1976).

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    V. N. Shapovalov, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 4, 27 (1974).

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    V. N. Shapovalov and N. B. Sukhomlin, Izv. Vyssh. Uchebn. Zaved., Fiz., No. 12, 100 (1974).

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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 40–45, December, 1976.

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Sukhomlin, N.B. Separation of variables in the diffusion equation. II. Soviet Physics Journal 19, 1559–1563 (1976). https://doi.org/10.1007/BF00890751

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Keywords

  • Diffusion Coefficient
  • Diffusion Equation
  • Symmetry Property
  • Complete Separation
  • Linear Diffusion