Skip to main content
SpringerLink
Log in

Local Solvability of Initial-Boundary Value Problem for One-Dimensional Equations of Polytropic Flows of Viscous Compressible Multifluids

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We consider the initial-boundary value problem governing unsteady polytropic motions of viscous compressible multifluids. We prove the existence and uniqueness of a strong solution to the problem. Bibliography: 11 titles.

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. N. A. Kucher, D. A. Prokudin, “Stationary solutions to the equations of a mixture of viscous compressible fluids” [in Russian], Sib. Zh. Ind. Mat. 12, No. 3, 52–65 (2009).

    MathSciNet  MATH  Google Scholar 

  2. N. A. Kucher, A. E. Mamontov, and D. A. Prokudin, “Stationary solutions to the equations of dynamics of mixtures of heat–conductive compressible viscous fluids,” Sib. Math. J. 53, No. 6, 1075–1088 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  3. A. E. Mamontov and D. A. Prokudin, “Solubility of a stationary boundary-value problem for the equations of motion of a one–temperature mixture of viscous compressible heat–conducting fluids,” Izv. Math. 78, No. 3, 554–579 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. E. Mamontov and D. A. Prokudin, “Solubility of initial-boundary value problem for the equations of polytropic motion of multicomponent viscous compressible fluids” [in Russian], Sib. Èlektron. Mat. Izv. 13, 541–583 (2016).

    MathSciNet  MATH  Google Scholar 

  5. A. E. Mamontov and D. A. Prokudin, “Viscous compressible multi-fluids: modeling and multi-d existence,” Methods Appl. Anal 20, No. 2, 179–195 (2013).

    MathSciNet  MATH  Google Scholar 

  6. A. V. Kazhikov and A. N. Petrov, “Well-posedness of the initial–boundary value problem for a model system of equations of a multicomponent mixture” [in Russian], Din. Splosh. Sredy 35, 61–73 (1978).

  7. A. N. Petrov, “Well-posedness of initial–boundary value problems for one–dimensional equations of mutually penetrating flows of ideal gases” [in Russian], Din. Splosh. Sredy 56, 105–121 (1982).

  8. A. V. Kazhikov, Selected Works. Mathematical Hydrodynamics [in Russian], Lavrentyev Inst. Hydrodynamics, Novosibirsk (2008).

    Google Scholar 

  9. I. Müller, “A thermodynamic theory of mixtures of fluids,” Arch. Ration. Mech. Anal 28, 1–39 (1968).

    Article  MathSciNet  MATH  Google Scholar 

  10. R. I. Nigmatulin, Dynamics of Multiphase Media. 1 [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  11. K. L. Rajagopal and L. Tao, Mechanics of Mixtures, World Scientific, Singapore (1995).

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lavrent’ev Institute of Hydrodynamics SB RAS, 15, Akad. Lavrent’eva pr, Novosibirsk, 630090, Russia

    A. E. Mamontov & D. A. Prokudin

  2. Novosibirsk State University, 1, Pirogova St, Novosibirsk, 630090, Russia

    A. E. Mamontov & D. A. Prokudin

Authors
  1. A. E. Mamontov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. A. Prokudin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. E. Mamontov.

Additional information

Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 17, No. 2, 2017, pp. 52-68.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mamontov, A.E., Prokudin, D.A. Local Solvability of Initial-Boundary Value Problem for One-Dimensional Equations of Polytropic Flows of Viscous Compressible Multifluids. J Math Sci 231, 227–242 (2018). https://doi.org/10.1007/s10958-018-3818-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-018-3818-9

Search

Navigation