Voir la notice de l'article provenant de la source Math-Net.Ru
@article{EMJ_2022_13_3_a1, author = {S. A. Budochkina and H. P. Vu}, title = {On an indirect representation of evolutionary equations in the form of {Birkhoff's} equations}, journal = {Eurasian mathematical journal}, pages = {23--32}, publisher = {mathdoc}, volume = {13}, number = {3}, year = {2022}, language = {en}, url = {http://geodesic.mathdoc.fr/item/EMJ_2022_13_3_a1/} }
TY - JOUR AU - S. A. Budochkina AU - H. P. Vu TI - On an indirect representation of evolutionary equations in the form of Birkhoff's equations JO - Eurasian mathematical journal PY - 2022 SP - 23 EP - 32 VL - 13 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/EMJ_2022_13_3_a1/ LA - en ID - EMJ_2022_13_3_a1 ER -
S. A. Budochkina; H. P. Vu. On an indirect representation of evolutionary equations in the form of Birkhoff's equations. Eurasian mathematical journal, Tome 13 (2022) no. 3, pp. 23-32. http://geodesic.mathdoc.fr/item/EMJ_2022_13_3_a1/
[1] S. A. Budochkina, “On a representation of an operator equation with first time derivative in the form of a $B_u$-Hamiltonian equation”, Differential Equations, 49:2 (2013), 176–186 | DOI | MR | Zbl
[2] S. A. Budochkina, V. M. Savchin, “On $B_u$-Hamiltonian equations in mechanics of infinite-dimensional systems”, Doklady Mathematics, 84:1 (2011), 525–526 | DOI | MR | Zbl
[3] S. A. Budochkina, V. M. Savchin, “On direct variational formulations for second order evolutionary equations”, Eurasian Mathematical Journal, 3:4 (2012), 23–34 | MR | Zbl
[4] S. A. Budotchkina, V. M. Savchin, “On indirect variational formulations for operator equations”, Journal of Function Spaces and Applications, 5:3 (2007), 231–242 | DOI | MR
[5] V. M. Filippov, Variational principles for nonpotential operators, Peoples' Friendship University of Russia, M., 1985 (in Russian) | MR
[6] V. M. Filippov, S. R. Mikhailova, Gondo Yake, “Construction of variational factors for quasilinear second order partial differential equations”, Computer Physics Communications, 126:1-2 (2000), 67–71 | DOI | MR | Zbl
[7] V. M. Filippov, V. M. Savchin, S. G. Shorokhov, “Variational principles for nonpotential operators”, Journal of Mathematical Sciences, 68:3 (1994), 275–398 | DOI | MR
[8] A. S. Galiullin, Inverse problems of dynamics, Nauka, M., 1981 (in Russian) | MR | Zbl
[9] A. S. Galiullin, “Invariance of action and inverse problems of dynamics”, Differential Equations, 20:8 (1984), 1318–1325 (in Russian) | MR
[10] A. S. Galiullin, “Generalizations of Hamiltonian systems”, Differential Equations, 24:5 (1988), 483–490 | MR | Zbl
[11] A. S. Galiullin, G. G. Gafarov, R. P. Malayshka, A. M. Khvan, “Analytical dynamics of Helmholtz, Birkhoff, Nambu systems”, Advances in Physical Sciences, M., 1997 (in Russian)
[12] M. T. Jenaliyev, M. I. Ramazanov, M. T. Kosmakova, Zh. M. Tuleutaeva, “On the solution to a two-dimensional heat conduction problem in a degenerate domain”, Eurasian Mathematical Journal, 11:3 (2020), 89–94 | DOI | MR | Zbl
[13] M. T. Jenaliyev, M. I. Ramazanov, M. G. Yergaliyev, “On an inverse problem for a parabolic equation in a degenerate angular domain”, Eurasian Mathematical Journal, 12:2 (2021), 25–38 | MR | Zbl
[14] R. M. Santilli, Foundations of theoretical mechanics, II: Birkhoffian generalization of Hamiltonian mechanics, Springer-Verlag, New-York–Berlin, 1983 | MR | Zbl
[15] V. M. Savchin, Mathematical methods of mechanics of infinite dimensional nonpotential systems, Peoples' Friendship University of Russia, M., 1991 (in Russian)
[16] V. M. Savchin, “An operator approach to Birkhoff's equations”, Bulletin of Peoples' Friendship University of Russia. Series Mathematics, 1995, no. 2 (2), 111–123 | Zbl
[17] V. M. Savchin, “Potential operators with the first time derivative and Hamiltonian systems”, Proceedings of the International Conference dedicated to Corresponding Member of RAS, Professor L.D. Kudryavtsev on the occasion of his 75th anniversary, v. 2, Peoples' Friendship University of Russia, M., 1998, 147–151 (in Russian)
[18] V. M. Savchin, S. A. Budochkina, “On the structure of a variational equation of evolution type with the second t-derivative”, Differential Equations, 39:1 (2003), 127–134 | DOI | MR | Zbl
[19] V. M. Savchin, S. A. Budochkina, “On the existence of a variational principle for an operator equation with the second derivative with respect to “time””, Mathematical Notes, 80:1 (2006), 83–90 | DOI | MR | Zbl
[20] M. I. Tleubergenov, D. T. Azhymbaev, “Stochastical problem of Helmholtz for Birkhoff systems”, Bulletin of the Karaganda University. Mathematics Series, 93:1 (2019), 78–87 | DOI
[21] M. I. Tleubergenov, G. T. Ibraeva, “On the solvability of the main inverse problem for stochastic differential systems”, Ukrainian Mathematical Journal, 71:1 (2019), 157–165 | DOI | MR | Zbl
[22] M. I. Tleubergenov, G. T. Ibraeva, “On inverse problem of closure of differential systems with degenerate diffusion”, Eurasian Mathematical Journal, 10:2 (2019), 93–102 | DOI | MR | Zbl
[23] M. I. Tleubergenov, G. T. Ibraeva, “On the closure of stochastic differential equations of motion”, Eurasian Mathematical Journal, 12:2 (2021), 82–89 | MR | Zbl