Geodesic
Classical solutions of hyperbolic differential-difference equation with shift by an arbitrary vector
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2023), pp. 34-40.

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

We construct three-parameter family of solutions in a half-space for the multidimensional hyperbolic differential-difference equation with shift operators of the general type acting on all spatial variables. Solutions are built using an operating scheme. We prove the theorem stating that these solutions are classical under the condition that the real part of the symbol of the differential-difference operator is positive. Classes of equations for which the indicated condition is satisfied are given.
Keywords: hyperbolic equation, differential-difference equation, classical solution
Mots-clés : Fourier transform. 
@article{IVM_2023_5_a3,
     author = {N. V. Zaitseva and A. B. Muravnik},
     title = {Classical solutions of hyperbolic differential-difference equation with shift by an arbitrary vector},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {34--40},
     publisher = {mathdoc},
     number = {5},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_5_a3/}
}
TY  - JOUR
AU  - N. V. Zaitseva
AU  - A. B. Muravnik
TI  - Classical solutions of hyperbolic differential-difference equation with shift by an arbitrary vector
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 34
EP  - 40
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_5_a3/
LA  - ru
ID  - IVM_2023_5_a3
ER  - 
%0 Journal Article
%A N. V. Zaitseva
%A A. B. Muravnik
%T Classical solutions of hyperbolic differential-difference equation with shift by an arbitrary vector
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 34-40
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_5_a3/
%G ru
%F IVM_2023_5_a3
N. V. Zaitseva; A. B. Muravnik. Classical solutions of hyperbolic differential-difference equation with shift by an arbitrary vector. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2023), pp. 34-40. http://geodesic.mathdoc.fr/item/IVM_2023_5_a3/

[1] Skubachevskii A.L., Elliptic functional-differential equations and applications, Birkhäuser, Basel–Boston–Berlin, 1997 | MR | Zbl

[2] Skubachevskii A.L., “Kraevye zadachi dlya ellipticheskikh funktsionalno-differentsialnykh uravnenii i ikh prilozheniya”, Uspekhi matem. nauk, 71:5(431) (2016), 3–112 | DOI | MR | Zbl

[3] Muravnik A.B., “Ellipticheskie zadachi s nelokalnym potentsialom, voznikayuschie v modelyakh nelineinoi optiki”, Matem. zametki, 105:5 (2019), 747–762 | DOI | MR | Zbl

[4] Muravnik A.B., “Ellipticheskie differentsialno-raznostnye uravneniya obschego vida v poluprostranstve”, Matem. zametki, 110:1 (2021), 90–98 | DOI | MR | Zbl

[5] Muravnik A.B., “Ellipticheskie differentsialno-raznostnye uravneniya s raznonapravlennymi sdvigami v poluprostranstve”, Ufimsk. matem. zhurn., 13:3 (2021), 107–115 | Zbl

[6] Muravnik A.B., “Ellipticheskie differentsialno-raznostnye uravneniya s nelokalnymi potentsialami v poluprostranstve”, Zhurn. vychisl. matem. i matem. fiz., 62:6 (2022), 987–993 | MR | Zbl

[7] Muravnik A.B., “Ellipticheskie uravneniya so sdvigami obschego vida v poluprostranstve”, Matem. zametki, 111:4 (2022), 571–580 | DOI | Zbl

[8] Vlasov V.V., “Korrektnaya razreshimost odnogo klassa differentsialnykh uravnenii s otklonyayuschimsya argumentom v gilbertovom prostranstve”, Izv. vuzov. Matem., 1996, no. 1, 22–35 | Zbl

[9] Iaakbariekh A., Sakbaev V.Zh., “Korrektnost zadachi dlya parabolicheskikh differentsialno-raznostnykh uravnenii so sdvigami vremennogo argumenta”, Izv. vuzov. Matem., 2015, no. 4, 17–25

[10] Muravnik A.B., “Funktsionalno-differentsialnye parabolicheskie uravneniya: integralnye predstavleniya i kachestvennye svoistva reshenii zadachi Koshi”, Sovremen. matem. Fundament. napravleniya, 52, 2014, 3–143

[11] Zarubin A.N., “Zadacha Koshi dlya differentsialno-raznostnogo nelokalnogo volnovogo uravneniya”, Differents. uravneniya, 41:10 (2005), 1406–1409 | MR | Zbl

[12] Vlasov V.V., Medvedev D.A., “Funktsionalno-differentsialnye uravneniya v prostranstvakh Soboleva i svyazannye s nimi voprosy spektralnoi teorii”, Sovremen. matem. Fundament. napravleniya, 30, 2008, 3–173

[13] Akbari Fallakhi A., Iaakbariekh A., Sakbaev V.Zh., “Korrektnost zadachi s nachalnymi usloviyami dlya giperbolicheskikh differentsialno-raznostnykh uravnenii so sdvigami vremennogo argumenta”, Differents. uravneniya, 52:3 (2016), 352–365 | DOI | MR | Zbl

[14] Zaitseva N.V., “O globalnykh klassicheskikh resheniyakh nekotorykh giperbolicheskikh differentsialno-raznostnykh uravnenii”, Dokl. RAN. Matem., informatika, protsessy upravleniya, 491:2 (2020), 44–46 | DOI | Zbl

[15] Zaitseva N.V., “Globalnye klassicheskie resheniya nekotorykh dvumernykh giperbolicheskikh differentsialno-raznostnykh uravnenii”, Differents. uravneniya, 56:6 (2020), 745–751 | DOI | Zbl

[16] Zaitseva N.V., “Classical solutions of hyperbolic differential-difference equations with several nonlocal terms”, Lobachevskii J. Math., 42:1 (2021), 231–236 | DOI | MR | Zbl

[17] Zaitseva N.V., “Giperbolicheskie differentsialno-raznostnye uravneniya s nelokalnymi potentsialami obschego vida”, Ufimsk. matem. zhurn., 13:3 (2021), 37–44 | Zbl

[18] Zaitseva N.V., “Klassicheskie resheniya giperbolicheskogo uravneniya s nelokalnym potentsialom”, Dokl. RAN. Matem., informatika, protsessy upravleniya, 498:3 (2021), 37–40 | DOI | Zbl

[19] Zaitseva N.V., “Klassicheskie resheniya giperbolicheskikh differentsialno-raznostnykh uravnenii v poluprostranstve”, Differents. uravneniya, 58:5 (2022), 628–637

[20] Gelfand I.M., Shilov G.E., “Preobrazovaniya Fure bystro rastuschikh funktsii i voprosy edinstvennosti resheniya zadachi Koshi”, Usp. matem. nauk, 8:6(58) (1953), 3–54 | MR | Zbl