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.
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Original Russian Text © A.D. Polyanin, S.A. Lychev, 2014, published in Doklady Akademii Nauk, 2014, Vol. 458, No. 6, pp. 663–666.
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Polyanin, A.D., Lychev, S.A. Various decomposition techniques for linear equations of continuum mechanics. Dokl. Phys. 59, 487–490 (2014). https://doi.org/10.1134/S1028335814100152