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@article{TRSPY_2018_300_a0, author = {A. V. Aksenov}, title = {Symmetries of fundamental solutions and their application in continuum mechanics}, journal = {Informatics and Automation}, pages = {7--18}, publisher = {mathdoc}, volume = {300}, year = {2018}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/TRSPY_2018_300_a0/} }
A. V. Aksenov. Symmetries of fundamental solutions and their application in continuum mechanics. Informatics and Automation, Modern problems and methods in mechanics, Tome 300 (2018), pp. 7-18. http://geodesic.mathdoc.fr/item/TRSPY_2018_300_a0/
[1] A. V. Aksenov, “Symmetries of linear partial differential equations and fundamental solutions”, Dokl. Math., 51:3 (1995), 329–331 | MR
[2] A. V. Aksenov, “Exact solutions describing one-dimensional isentropic flow of a polytropic gas”, Proc. Steklov Inst. Math., 223 (1998), 143–148 | MR | Zbl
[3] A. V. Aksenov, “Symmetries and invariant solutions of absolutely unstable media equations”, Phys. At. Nucl., 63 (2000), 677–679 | DOI | MR
[4] A. V. Aksenov, “Development of periodic perturbations in absolutely unstable media”, Nonlinearity in Modern Natural Science, LKI, Moscow, 2009, 134–151 (in Russian)
[5] A. V. Aksenov, “Nonlinear periodic waves in a gas”, Fluid Dyn., 47 (2012), 636–646 | DOI | MR
[6] Bluman G., “Simplifying the form of Lie groups admitted by a given differential equation”, J. Math. Anal. Appl., 145:1 (1990), 52–62 | DOI | MR
[7] Copson E. T., “On the Riemann–Green function”, Arch. Ration. Mech. Anal., 1 (1958), 324–348 | DOI | MR
[8] R. Courant, K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience, New York, 1948 | MR
[9] D. V. Georgievskii, “An extended Galerkin representation for a transversely isotropic linearly elastic medium”, J. Appl. Math. Mech., 79 (2015), 618–621 | DOI | MR
[10] J. Hadamard, Le problème de Cauchy et les équations aux dérivées partielles linéaires hyperboliques, Hermann, Paris, 1932 | MR
[11] N. Kh. Ibragimov, “Group analysis of ordinary differential equations and the invariance principle in mathematical physics (on the 150th anniversary of Sophus Lie)”, Russ. Math. Surv., 47:4 (1992), 89–156 | DOI | MR | Zbl
[12] L. V. Ovsiannikov, “Group properties of S. A. Chaplygin's equation”, Prikl. Mekh. Tekh. Fiz., 1960, no. 3, 126–145
[13] L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic, New York, 1982 | MR | MR
[14] B. Riemann, Ueber die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite, Abh. König. Ges. Wiss. Gött., 8, Dieterichischen Buchhandlung, Göttingen, 1860
[15] V. S. Vladimirov, Generalized Functions in Mathematical Physics, Mir, Moscow, 1979 | MR | MR
[16] S. K. Zhdanov, B. A. Trubnikov, Quasi-gas Unstable Media, Nauka, Moscow, 1991 (in Russian)