Geodesic
Stability of a solution to one combined mixed problem for the Klein–Gordon–Fock equation with a variable coefficient
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2021), pp. 3-10 
M. F. Abdukarimov. Stability of a solution to one combined mixed problem for the Klein–Gordon–Fock equation with a variable coefficient. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2021), pp. 3-10. http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a0/
@article{VMUMM_2021_2_a0,
     author = {M. F. Abdukarimov},
     title = {Stability of a solution to one combined mixed problem for the {Klein{\textendash}Gordon{\textendash}Fock} equation with a variable coefficient},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--10},
     year = {2021},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a0/}
}
TY  - JOUR
AU  - M. F. Abdukarimov
TI  - Stability of a solution to one combined mixed problem for the Klein–Gordon–Fock equation with a variable coefficient
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2021
SP  - 3
EP  - 10
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a0/
LA  - ru
ID  - VMUMM_2021_2_a0
ER  - 
%0 Journal Article
%A M. F. Abdukarimov
%T Stability of a solution to one combined mixed problem for the Klein–Gordon–Fock equation with a variable coefficient
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2021
%P 3-10
%N 2
%U http://geodesic.mathdoc.fr/item/VMUMM_2021_2_a0/
%G ru
%F VMUMM_2021_2_a0

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

The paper studies one combined mixed problem for the Klein–Gordon–Fock equation with a variable coefficient. The solvability of the problem under consideration is proved. In addition to solvability, it is also substantiated that the solution to the studied mixed problem is stable with respect to an additive perturbation of the coefficient, as well as with respect to the boundary conditions and the right-hand side of the equation.

[1] Lions Zh.L., Upravlenie singulyarnymi raspredelennymi sistemami, Nauka, M., 1987

[2] Ladyzhenskaya O.A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973

[3] Abdukarimov M.F., Kritskov L.V., “Zadacha granichnogo upravleniya dlya odnomernogo uravneniya Kleina–Gordona–Foka s peremennym koeffitsientom. Sluchai upravleniya smescheniem na dvukh kontsakh”, Differents. uravneniya, 49:8 (2013), 1036–1046 | MR | Zbl

[4] Abdukarimov M.F., Kritskov L.V., “Zadacha granichnogo upravleniya dlya odnomernogo uravneniya Kleina–Gordona–Foka s peremennym koeffitsientom. Sluchai upravleniya smescheniem na odnom kontse”, Differents. uravneniya, 49:6 (2013), 759–771 | MR | Zbl

[5] Kritskov L.V., Abdukarimov M.F., “Granichnoe upravlenie smescheniem na odnom kontse pri svobodnom vtorom dlya protsessa, opisyvaemogo telegrafnym uravneniem s peremennym koeffitsientom”, Dokl. RAN, 450:6 (2013), 640–643 | MR | Zbl

[6] Kritskov L.V., “O zadachakh granichnogo upravleniya dlya odnomernogo uravneniya Kleina–Gordona–Foka s summiruemym koeffitsientom”, Differents. uravneniya, 51:5 (2015), 688–701 | Zbl

[7] Abdukarimov M.F., Nekotorye zadachi granichnogo upravleniya smescheniem dlya telegrafnogo uravneniya s peremennym koeffitsientom, Dushanbe, 2018

[8] Abdukarimov M.F., “Ob ustoichivosti resheniya odnoi smeshannoi zadachi dlya telegrafnogo uravneniya”, Vestn. Tadzhik. nats. un-ta. Ser. estestv. nauk, 2017, no. 1/5, 116–122

[9] Ilin V.A., “O razreshimosti smeshannykh zadach dlya giperbolicheskogo i parabolicheskogo uravnenii”, Uspekhi matem. nauk, 15:2(92) (1960), 97–154

[10] Abdukarimov M.F., “O granichnom upravlenii uprugoi siloi na odnom kontse pri zakreplennom vtorom protsessa vynuzhdennykh kolebanii struny”, Dokl. Akad. nauk Respubliki Tadzhikistan, 58:10 (2015), 894–900

[11] Abdukarimov M.F., “O granichnom upravlenii uprugimi silami na dvukh kontsakh protsessa vynuzhdennykh kolebanii struny za minimalnyi promezhutok vremeni”, Dokl. Akad. nauk Respubliki Tadzhikistan, 60:5–6 (2017), 205–211

[12] Abdukarimov M.F., Abdukarimzoda A.K., “Razreshimost odnoi smeshannoi zadachi dlya uravneniya vynuzhdennykh kolebanii struny v ogranichennoi oblasti”, Mat-ly nauchno-prakticheskoi konf. “IX Lomonosovskie chteniya” (Dushanbe, 2019), 8–13

[13] Ilin V.A., “Granichnoe upravlenie protsessom kolebanii na dvukh kontsakh v terminakh obobschennogo resheniya volnovogo uravneniya s konechnoi energiei”, Differents. uravneniya, 36:11 (2000), 1513–1528 | MR