Russian Journal of Mathematical Physics

, Volume 26, Issue 1, pp 130–134 | Cite as

On a Deep Bed Filtration Problem with Finite Blocking Time

  • L. I. KuzminaEmail author
  • V. E. NazaikinskiiEmail author
  • Yu. V. OsipovEmail author
Short Communications


We consider an initial–boundary value problem for a simple semilinear filtration equation with nonunique characteristics and prove that uniqueness nevertheless holds for the solution of this problem. The solution is then constructed by quadratures.


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  1. 1.
    Z. You et al., “Exact Solution for Long–Term Size Exclusion Suspension–Colloidal Transport in Porous Media,” Abstr. Appl. Anal. 2013, 1–9, Article ID 680693 (2013).Google Scholar
  2. 2.
    Z. You et al., “Asymptotic Model for Deep Bed Filtration,” Chem. Eng. J. 258, 374–385 (2014).CrossRefGoogle Scholar
  3. 3.
    A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Pergamon Press, Oxford, England, 1963).zbMATHGoogle Scholar
  4. 4.
    A. N. Tikhonov and A. A. Samarskii, “On Discontinuous Solutions of a Quasilinear Equation of First Order,” Dokl. Akad. Nauk SSSR 99, 27–30 (1954).MathSciNetGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.Ishlinsky Institute for Problems in Mechanics of the Russian Academy of SciencesMoscowRussia
  3. 3.Moscow Institute of Physics and Technology (State University)Dolgoprudny, Moscow OblastRussia
  4. 4.Moscow State University of Civil EngineeringMoscowRussia

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