Skip to main content
Log in

Various decomposition techniques for linear equations of continuum mechanics

Doklady Physics Aims and scope

Cite this article


Various methods of decomposition of a sufficiently general linear set of equations, special cases of which are frequently encountered in continuum mechanics, are described. These methods are based on splitting the sets of coupled 3D equations into several simpler independent equations. In addition to the firstorder decomposition, we also considered higher order decompositions. Examples of the decomposition of sets of equations describing slow motions of viscous and viscoelastic incompressible fluids and viscous compressible barotropic fluids and gases are presented. The obtained results can be used for the exact or numerical solution of 3D problems of continuum mechanics and physics.

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

Access this article

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


  1. G. Bachelor, Introduction to Liquid Dynamics (Mir, Moscow, 1973) [in Russian].

    Google Scholar 

  2. J. Happel and G. Brener, Hydrodynamics at Low Reynolds Numbers (Mir, Moscow, 1976) [in Russian].

    Google Scholar 

  3. A. D. Polyanin and A. I. Zhurov, Int. J. Non-Linear Mech. 49, 77 (2013).

    Article  ADS  Google Scholar 

  4. A. D. Polyanin and A. V. Vyaz’min, Teor. Osn. Khim. Tekhnol. 47(4), 386 (2013).

    Google Scholar 

  5. I. I. Lipatov and A. D. Polyanin, Dokl. Phys. 58(3), 116 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  6. V. Novatskii, Elasticity Theory (Mir, Moscow, 1975) [in Russian].

    Google Scholar 

  7. M. E. Gurtin and E. Sternberg, Arch. Ration. Mech. and Anal. 11(1), 291 (1962).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. M. E. Gurtin, The Linear Theory of Elasticity in Encyclopedia of Physics (Springer, Berlin, 1972), Vol. VIa/2.

    Google Scholar 

  9. E. Madenci and E. Oterkus, Peridynamic Theory and Its Applications (Springer, Berlin, 2014).

    Book  MATH  Google Scholar 

  10. D. A. W. Pecknold, J. Elasticity 1(2), 171 (1971).

    Article  Google Scholar 

  11. L. Morino, Comput. Mech., No. 1, 65 (1986).

    Google Scholar 

  12. M. E. Gurtin, Arch. Ration. Mech. & Anal. 9(1), 225 (1962).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  13. S. A. Lychev, Bull. Russ. Acad. Sci.: Solid Mech., No. 5, 95 (2008).

    Google Scholar 

  14. S. A. Lychev, A. V. Manzhirov, and S. V. Yuber, Bull. Russ. Acad. Sci.: Solid Mech., No. 4, 138 (2010).

    Google Scholar 

  15. A. D. Polyanin and S. A. Lychev, Dokl. Phys. 59(3), 148 (2014).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to A. D. Polyanin.

Additional information

Original Russian Text © A.D. Polyanin, S.A. Lychev, 2014, published in Doklady Akademii Nauk, 2014, Vol. 458, No. 6, pp. 663–666.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Polyanin, A.D., Lychev, S.A. Various decomposition techniques for linear equations of continuum mechanics. Dokl. Phys. 59, 487–490 (2014).

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: