Abstract
The process is considered of establishing the equilibrium spatial distribution of the concentration of particles in a one-dimensional bounded space region, subjected to a constant force normal to impermeable region boundaries. This process is described by the solution of the third boundary-value problem with homogeneous boundary conditions for the two-dimensional parabolic equation. It is shown that the found solution to the seemingly well-known problem of mathematical physics, but being of great importance in applications, cannot be obtained using theGreen’s function of this problem, known in the literature.
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References
V. I. Ivanov and A. I. Livashvili, “Electrostriction Mechanism of Radiation Self-Action in Liquid with Nanoparticles,” VestnikNGU. Ser. Fiz. 4(2), 58 (2009).
V. I. Ivanov, A. A. Kuzin, and A. I. Livashvili, “Thermally Induced Self-Action of the Gaussian Radiation Beam in a Liquid Dispersed Medium,” VestnikNGU. Ser. Fiz. 5(1), 5 (2010).
A. D. Polyanin, Handbook on Linear Equations of Mathematical Physics (Fizmatlit, Moscow, 2001) [in Rissian].
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Original Russian Text © V.I. Krylov, A.A. Rukhadze, V.I. Nefedov, 2017, published in Kratkie Soobshcheniya po Fizike, 2017, Vol. 44, No. 2, pp. 14–19.
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Krylov, V.I., Rukhadze, A.A. & Nefedov, V.I. On a partial solution of the diffusion equation. Bull. Lebedev Phys. Inst. 44, 36–39 (2017). https://doi.org/10.3103/S1068335617020038
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DOI: https://doi.org/10.3103/S1068335617020038