On unique solvability of the system of gravitational-gyroscopic waves in the Boussinesq approximation
Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 2, pp. 16-23.

Voir la notice de l'article provenant de la source Math-Net.Ru

Initial boundary value problem is studied for the system of gravitational-gyroscopic waves in the Boussinesq approximation, i. e. for the integro-differential system of equations with partial derivatives. The existence of a unique solution is proved for the problem by the methods of the theory of degenerate evolution equations in Banach spaces.
Keywords: system of gravitational-gyroscopic waves, system of internal waves, Boussinesq approximation, initial boundary value problem, degenerate evolution equation, equation with memory.
@article{CHFMJ_2016_1_2_a1,
     author = {L. V. Borel' and V. E. Fedorov},
     title = {On unique solvability of the system of gravitational-gyroscopic waves in the {Boussinesq} approximation},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {16--23},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_2_a1/}
}
TY  - JOUR
AU  - L. V. Borel'
AU  - V. E. Fedorov
TI  - On unique solvability of the system of gravitational-gyroscopic waves in the Boussinesq approximation
JO  - Čelâbinskij fiziko-matematičeskij žurnal
PY  - 2016
SP  - 16
EP  - 23
VL  - 1
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_2_a1/
LA  - ru
ID  - CHFMJ_2016_1_2_a1
ER  - 
%0 Journal Article
%A L. V. Borel'
%A V. E. Fedorov
%T On unique solvability of the system of gravitational-gyroscopic waves in the Boussinesq approximation
%J Čelâbinskij fiziko-matematičeskij žurnal
%D 2016
%P 16-23
%V 1
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_2_a1/
%G ru
%F CHFMJ_2016_1_2_a1
L. V. Borel'; V. E. Fedorov. On unique solvability of the system of gravitational-gyroscopic waves in the Boussinesq approximation. Čelâbinskij fiziko-matematičeskij žurnal, Tome 1 (2016) no. 2, pp. 16-23. http://geodesic.mathdoc.fr/item/CHFMJ_2016_1_2_a1/

[1] G. A. Demidenko, S. V. Uspenskii, Partial Differential Equations and Systems not Solvable with Respect to the Highest-Order Derivative, Marcel Dekker, New York-Basel, 2003, 490 pp. | MR | MR | Zbl

[2] M. V. Falaleev, S. S. Orlov, “Vyrozhdennye integro-differentsialnye uravneniya spetsialnogo vida v banakhovykh prostranstvakh i ikh prilozheniya”, Vestn. Yuzh.-Ural. gos. un-ta. Ser. «Mat. modelirovanie i programmirovanie», 2011, no. 7, No 4 (211), 100–110 | Zbl

[3] M. V. Falaleev, S. S. Orlov, “Integro-differential equations with degeneration in Banach spaces and their applications in the mathematical elasticity theory”, News of Irkutsk State University. Mathematics, 4:1 (2011), 118–134 (In Russ.) | Zbl

[4] M. V. Falaleev, S. S. Orlov, “Degenerate Integro-Differential Operators in Banach Spaces and Their Applications”, Russian Mathematics, 55:10 (2011), 59–69 | DOI | MR | Zbl

[5] M. V. Falaleev, “Integro-differential equations with a Fredholm operator at the highest derivative in Banach spaces and their applications”, News of Irkutsk State University. Mathematics, 5:5 (2012), 90–102 (In Russ.) | Zbl

[6] O. A. Stakheeva, “Local solvability of a class of linear equations with memory”, Bulletin of Chelyabinsk State University, 2009, no. 11, 20 (158), 70–76 (In Russ.) | MR | Zbl

[7] V. E. Fedorov, O. A. Stakheeva, “On solvability of linear Sobolev type equation with memory effect”, Nonclassical equations of mathematical physics, Sobolev Institute of Mathematics of SB RAS Publ., Novosibirsk, 2010, 245–261 (In Russ.)

[8] V. E. Fedorov, L. B. Borel, “On solvability of linear evolution equations with memory effects”, News of Irkutsk State University. Mathematics, 10 (2014), 106–124 (In Russ.) | Zbl

[9] V. E. Fedorov, O. A. Stakheeva, “On the local existence of solutions of equation with memory not solvable with respect to the time derivative”, Mathematical Notes, 98:3 (2015), 472–483 | DOI | DOI | MR | Zbl

[10] V. E. Fedorov, E. A. Omelchenko, “On solvability of some classes of Sobolev type equations with delay”, Functional Differential Equations, 2011 vol 18, no. 3–4, 187–199 | MR | Zbl

[11] V. E. Fedorov, E. A. Omelchenko, “Inhomogeneous linear Sobolev type equations with delay”, Siberian Mathematical Journal, 53:2 (2012), 335–344 | DOI | MR | Zbl

[12] “Linear equations of the Sobolev type with integral delay operator”, Russian Mathematics, 58:1 (2014), 60–69 | DOI | MR | Zbl

[13] V. E. Fedorov, L. B. Borel, “Solvability of loaded linear evolution equations with a degenerate operator at the derivative”, St. Petersburg Mathematical Journal, 26:3 (2015), 487–497 | DOI | MR | Zbl

[14] L. B. Borel, “On solvability of degenerate loaded systems of equations”, Mathematical notes of North-Eastern Federal University, 22:4 (88) (2015), 3–11 (In Russ.)

[15] V. E. Fedorov, D. M. Gordievskikh, “Resolving operators of degenerate evolution equations with fractional derivative with respect to time”, Russian Mathematics, 59:1 (2015), 60–70 | DOI | MR | Zbl

[16] V. E. Fedorov, D. M. Gordievskikh, “Solutions of initial-boundary value problems for some degenerate time-fractional order systems of equations”, News of Irkutsk State University. Mathematics, 12 (2015), 12–22 (In Russ.) | Zbl

[17] V. E. Fedorov, D. M. Gordievskikh, M. V. Plekhanova, “Equations in Banach spaces with a degenerate operator under a fractional derivative”, Differential Equations, 51:10 (2015), 1360–1368 | DOI | DOI | MR | Zbl

[18] G. A. Sviridyuk, V. E. Fedorov, Linear Sobolev Type Equations and Degenerate Semigroups of Operators, VSP, Utrecht–Boston, 2003, 216+vii pp. | MR | Zbl

[19] S. L. Sobolev, “On a new problem of mathematical physics”, Izvestiya Akademii nauk SSSR. Seriya matematicheskaya, 18:1 (1954), 3–50 (In Russ.) | Zbl

[20] V. E. Fedorov, N. D. Ivanova N.D., “Nonlinear evolution inverse problem for some Sobolev type equations”, Siberian Electronic Mathematical Reports, 8, Proceedings of the Second International School-Conference, p. I (2011), 363–378 (In Russ.) http://semr.math.nsc.ru/v8/c182-410.pdf