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A diffusion problem in a region with a moving boundary

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Abstract

We consider the first linear diffusion problem in a semiinfinite region with a boundary moving in accordance with a quadratic law. For the case of uniformly decelerating motion of the boundary, the solution of the problem is obtained by the Green's function, method under the most general boundary conditions; the solution of the problem for the case of uniformly accelerated motion of the boundary is obtained by an operator method.

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Literature cited

  1. B. Ya. Lyubov, Kinetic Theory of Phase Transitions [in Russian], Metallurgiya (1969).

  2. G. N. Polozhii, Equations of Mathematical Physics [in Russian], Vysshaya Shkola (1964).

  3. N. N. Lebedev, Special Functions and Their Applications [in Russian], Fizmatgiz (1963).

  4. V. A. Ditkin and L. P. Trudnikov, Handbook of Operational Calculus [in Russian], Vysshaya Shkola (1965).

  5. G. D. Yakovleva, Tables of Airy Functions and Their Derivatives [in Russian], Nauka (1969).

  6. G. A. Grinberg, Prikl. Matem. Mekh.,33, No. 6 (1969).

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Authors and Affiliations

  1. V. I. Lenin Moscow State Pedagogical Institute, USSR

    É. M. Kartashov, B. Ya. Lyubov & G. M. Bartenev

Authors
  1. É. M. Kartashov
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  2. B. Ya. Lyubov
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  3. G. M. Bartenev
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Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 102–110, December, 1970.

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Kartashov, É.M., Lyubov, B.Y. & Bartenev, G.M. A diffusion problem in a region with a moving boundary. Soviet Physics Journal 13, 1641–1647 (1970). https://doi.org/10.1007/BF00820122

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  • DOI: https://doi.org/10.1007/BF00820122

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