Geodesic
Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1571-1579 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An initial boundary-value problem for a quasilinear system of partial differential equations with a nonlocal boundary condition involving a delayed argument is considered. The existence of a unique solution to this problem is proved by reducing it to a system of nonlinear integral-functional equations. The inverse problem of finding a solution-dependent coefficient of the system from additional information on a solution component specified at a fixed point of space as a function of time is formulated. The uniqueness of the solution of the inverse problem is proved. The proof is based on the derivation and analysis of an integral-functional equation for the difference between two solutions of the inverse problem. 
@article{ZVMMF_2014_54_10_a3,
     author = {A. M. Denisov},
     title = {Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1571--1579},
     year = {2014},
     volume = {54},
     number = {10},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a3/}
}
TY  - JOUR
AU  - A. M. Denisov
TI  - Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2014
SP  - 1571
EP  - 1579
VL  - 54
IS  - 10
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a3/
LA  - ru
ID  - ZVMMF_2014_54_10_a3
ER  - 
%0 Journal Article
%A A. M. Denisov
%T Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2014
%P 1571-1579
%V 54
%N 10
%U http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a3/
%G ru
%F ZVMMF_2014_54_10_a3
A. M. Denisov. Inverse problem for a quasilinear system of partial differential equations with a nonlocal boundary condition. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 10, pp. 1571-1579. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_10_a3/

[1] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Izd-vo MGU, M., 1999

[2] Denisov A. M., “Inverse problem for a hyperbolic equation with nonlocal boundary condition containing a delay argument”, Proc. Steklov Institute of Mathematics, 280, 2013, 51–58 | DOI

[3] Denisov A. M., Shirkova E. Yu., “Obratnaya zadacha dlya kvazilineinogo giperbolicheskogo uravneniya s nelokalnym kraevym usloviem, soderzhaschim zapazdyvayuschii argument”, Differents. ur-niya, 49:9 (2013), 1091–1099

[4] Denisov A. M., “Edinstvennost opredeleniya nelineinogo koeffitsienta sistemy uravnenii v chastnykh proizvodnykh v malom i v tselom”, Dokl. AN, 338:4 (1994), 444–447

[5] Denisov A. M., “Edinstvennost resheniya zadachi opredeleniya nelineinogo koeffitsienta sistemy uravnenii v chastnykh proizvodnykh v malom i v tselom”, Sibirsk. matem. zh., 36:1 (1995), 60–71

[6] Cannon J. R., DuChateau P., “An inverse problem for an unknown source term in a wave equation”, SIAM J. Appl. Math., 43:3 (1983), 553–564 | DOI

[7] Cavaterra C., “An inverse problem for semilinear wave equation”, Boll. Un. Mat. Ital. (B), 2:3 (1988), 695–711

[8] Graselli M., “Local existence and uniqueness for a quasilinear hyperbolic inverse problem”, Appl. Anal., 32:1 (1989), 15–30 | DOI

[9] Lorenzi A., Paparoni E., “An inverse problem arising in the theory of absorption”, Appl. Anal., 36:2 (1990), 249–263 | DOI

[10] Tuikina S. R., “O edinstvennosti resheniya odnoi obratnoi zadachi dlya polulineinoi sistemy uravnenii pervogo poryadka”, Vest. Mosk. un-ta. Ser. 15. Vychisl. matem. i kiber., 1996, no. 2, 12–18

[11] Shcheglov A. Yu., “The inverse problem of determination of a nonlinear source in a hyperbolic equation”, J. Inverse and Ill-Posed Problems, 6:6 (1998), 625–644 | DOI

[12] Denisov A. M., “Suschestvovanie resheniya obratnoi zadachi dlya kvazilineinogo uravneniya giperbolicheskogo tipa”, Differents. ur-niya, 38:9 (2002), 1155–1164