Geodesic
Inverse problems for nonlinear stationary equations
Matematičeskie zametki SVFU, Tome 23 (2016) no. 2, pp. 65-77 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Identification of the unknown constant coefficient in the main term of the partial differential equation $-kM\psi_1(u)+g(x)\psi_2(u)=f(x)$ with the Dirichlet boundary condition is investigated. Here $\psi_i(u),\quad i=1,2,$ is a nonlinear increasing function of $u$ and $M$ is a second-order linear elliptic operator. The coefficient $k$ is recovered on the base of additional integral boundary data. The existence and uniqueness of the solution to the inverse problem with a function u and a positive real number k is proved.
Keywords: inverse problem, boundary value problem, second-order elliptic equation, existence and uniqueness theorem
Mots-clés : filtration. 
@article{SVFU_2016_23_2_a4,
     author = {A. Sh. Lyubanova},
     title = {Inverse problems for nonlinear stationary equations},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {65--77},
     year = {2016},
     volume = {23},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2016_23_2_a4/}
}
TY  - JOUR
AU  - A. Sh. Lyubanova
TI  - Inverse problems for nonlinear stationary equations
JO  - Matematičeskie zametki SVFU
PY  - 2016
SP  - 65
EP  - 77
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SVFU_2016_23_2_a4/
LA  - ru
ID  - SVFU_2016_23_2_a4
ER  - 
%0 Journal Article
%A A. Sh. Lyubanova
%T Inverse problems for nonlinear stationary equations
%J Matematičeskie zametki SVFU
%D 2016
%P 65-77
%V 23
%N 2
%U http://geodesic.mathdoc.fr/item/SVFU_2016_23_2_a4/
%G ru
%F SVFU_2016_23_2_a4
A. Sh. Lyubanova. Inverse problems for nonlinear stationary equations. Matematičeskie zametki SVFU, Tome 23 (2016) no. 2, pp. 65-77. http://geodesic.mathdoc.fr/item/SVFU_2016_23_2_a4/

[1] Alessandrini G., Caburro R., “The local Calderon problem and the determination at the boundary of the conductivity”, Commun. Partial Differ. Equ., 34 (2009), 918–936 | DOI | MR | Zbl

[2] Calderon A. P., “On an inverse boundary value problem”, Seminar on numerical analysis and its applications to continuum physics, Soc. Brazil. Mat., Rio de Janeiro, 1980, 65–73 | MR

[3] Klibanov M. V., Timonov A., Carleman estimates for coefficient inverse problems and numerical applications, VSP, Utrecht, 2004 | MR | Zbl

[4] Lyubanova A. Sh., “Identification of a constant coefficient in an elliptic equation”, Appl. Anal., 2008, 1121–1128 | DOI | MR | Zbl

[5] Lyubanova A. Sh., “On an inverse problem for quasi-linear elliptic equation”, Zh. Sib. Fed. Univ., Mat. Fiz, 8:1 (2015), 38–48 | MR

[6] Nachman A., Street B., “Reconstruction in the Calderon problem with partial data”, Commun. Partial Differ. Equ., 35 (2010), 375–390 | DOI | MR | Zbl

[7] Nakamura G., Tanuma K., “A nonuniqueness theorem for inverse boundary value problem in elasticity”, SIAM J. Appl. Math., 56 (1996), 602–610 | DOI | MR | Zbl

[8] Ladyzhenskaya O. A. and Uraltseva N. N., Linear and quasilinear elliptic equations, Math. Sci. Eng., 46, Acad. Press, New York and London, 1968 | MR | MR | Zbl

[9] Gaevski Kh., Greger K., and Zakharias K., Nonlinear operator equations and operator differential equations, Mir, Moscow, 1978

[10] Lions J.-L. and Majenes E., Nonhomogeneous boundary value problams and its application, Mir, Moscow, 1968

[11] Prilepko A. I., Orlovsky D. G., Vasin I. A., Methods for solving inverse problems in mathematical physics, Marcel Dekker, Inc., New York, 2000 | MR | Zbl

[12] Sveshnikov A. G., Al'shin A. B., Korpusov M. O., and Pletner Yu. D., Linear and nonlinear equations of Sobolev type, Fizmatlit, Moscow, 2007