Skip to main content
SpringerLink
Log in

On a partial solution of the diffusion equation

  • Published:
Bulletin of the Lebedev Physics Institute Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. I. Ivanov and A. I. Livashvili, “Electrostriction Mechanism of Radiation Self-Action in Liquid with Nanoparticles,” VestnikNGU. Ser. Fiz. 4(2), 58 (2009).

    Google Scholar 

  2. 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).

    Google Scholar 

  3. A. D. Polyanin, Handbook on Linear Equations of Mathematical Physics (Fizmatlit, Moscow, 2001) [in Rissian].

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Far Eastern State Transport University, ul. Sarysheva 47, Khabarovsk, 680021, Russia

    V. I. Krylov

  2. Prokhorov General Physics Institute, Russian Academy of Sciences, ul. Vavilova 38, Moscow, 119991, Russia

    A. A. Rukhadze

  3. Moscow State Technical University of Radio Engineering, Electronics, and Automation, pr. Vernadskogo 78, Moscow, 119454, Russia

    V. I. Nefedov

Authors
  1. V. I. Krylov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. A. Rukhadze
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. I. Nefedov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Rukhadze.

Additional information

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.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068335617020038

Keywords

Search

Navigation