Boundary value problems for one pseudohyperbolic equation in a quarter plane
Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 3-23.

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

We consider general boundary value problems for one pseudohyperbolic equation in a quarter plane. We assume that the boundary value problems satisfy the Lopatinskii condition. We prove theorems on unique solvability in an anisotropic Sobolev space and establish some estimates for solutions.
@article{MT_2021_24_2_a0,
     author = {L. N. Bondar' and G. V. Demidenko},
     title = {Boundary value problems for one pseudohyperbolic equation in a quarter plane},
     journal = {Matemati\v{c}eskie trudy},
     pages = {3--23},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2021_24_2_a0/}
}
TY  - JOUR
AU  - L. N. Bondar'
AU  - G. V. Demidenko
TI  - Boundary value problems for one pseudohyperbolic equation in a quarter plane
JO  - Matematičeskie trudy
PY  - 2021
SP  - 3
EP  - 23
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2021_24_2_a0/
LA  - ru
ID  - MT_2021_24_2_a0
ER  - 
%0 Journal Article
%A L. N. Bondar'
%A G. V. Demidenko
%T Boundary value problems for one pseudohyperbolic equation in a quarter plane
%J Matematičeskie trudy
%D 2021
%P 3-23
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2021_24_2_a0/
%G ru
%F MT_2021_24_2_a0
L. N. Bondar'; G. V. Demidenko. Boundary value problems for one pseudohyperbolic equation in a quarter plane. Matematičeskie trudy, Tome 24 (2021) no. 2, pp. 3-23. http://geodesic.mathdoc.fr/item/MT_2021_24_2_a0/

[1] Besov O. V., Ilin V. P., Nikolskii S. M., Integralnye predstavleniya funktsii i teoremy vlozheniya, Nauka, M., 1975

[2] Vlasov V. Z., Tonkostennye uprugie sterzhni, Stroiizdat, M.–L., 1940

[3] Gerasimov S. I., Erofeev V. I., Zadachi volnovoi dinamiki elementov konstruktsii, FGUP «RFYaTs-VNIIEF», Sarov, 2014

[4] Demidenko G. V., Uspenskii S. V., Uravneniya i sistemy, ne razreshennye otnositelno starshei proizvodnoi, Nauchnaya kniga, Novosibirsk, 1998

[5] Demidenko G. V., “Usloviya razreshimosti zadachi Koshi dlya psevdogiperbolicheskikh uravnenii”, Sib. matem. zhurn., 56:6 (2015), 1289–1303 | Zbl

[6] Demidenko G. V., Prostranstva Soboleva i obobschennye resheniya, Uchebnoe posobie, RITs NGU, Novosibirsk, 2015

[7] Demidenko G. V., Kudryavtsev A. A., “Kraevye zadachi v chetverti ploskosti dlya uravneniya Releya — Bishopa”, Matem. zametki SVFU, 28:3 (2021), 5–18

[8] Dyuzheva A. V., “Zadacha s integralnym usloviem I roda dlya uravneniya chetvertogo poryadka”, Vestn. SamU. Estestvennonauchn. ser., 25:1 (2019), 21–31 | Zbl

[9] Shabat B. V., Vvedenie v kompleksnyi analiz, Nauka, M., 1969

[10] Sobolev S. L., Izbrannye trudy, v. 1, Uravnenie matematicheskoi fiziki. Vychislitelnaya matematika i kubaturnye formuly, eds. Demidenko G. V., Vaskevicha V. L., Izd-vo In-ta matematiki, filial «Geo» Izd-va SO RAN, Novosibirsk, 2003

[11] Umarov Kh. G., “Zadacha Koshi dlya uravneniya krutilnykh kolebanii nelineino-uprugogo sterzhnya beskonechnoi dliny”, Prikl. matem. i mekh., 83:2 (2019), 249–264 | Zbl

[12] Uspenskii S. V., Demidenko G. V., Perepelkin V. G., Teoremy vlozheniya i prilozheniya k differentsialnym uravneniyam, Nauka, Novosibirsk, 1984

[13] Fedotov I. A., Polyanin A. D., Shatalov M. Yu., Tenkam E. M., “Prodolnye kolebaniya sterzhnya Releya — Bishopa”, Dokl. RAN, 435:5 (2010), 613–618 | Zbl

[14] Bishop R. E. D., “Longitudinal waves in beams”, Aeronautical Quarterly, 3:4 (1952), 280–293 | DOI

[15] Fedotov I., Shatalov M., Marais J., “Hyperbolic and pseudo-hyperbolic equations in the theory of vibration”, Acta Mechanica, 227:11 (2016), 3315–3324 | DOI | Zbl

[16] Fedotov I., Volevich L. V., “The Cauchy problem for hyperbolic equations not resolved with respect to the highest time derivative”, Russ. J. Math. Phys., 13:3 (2006), 278–292 | DOI | Zbl

[17] Rao J. S., Advanced Theory of Vibration, Wiley Eastern, New Delhi, 1992