This article is cited in 3 scientific papers (total in 3 papers)
On an inverse problem for quasi-linear elliptic equation
Anna Sh. Lyubanova
Institute of Space and Information Technology, Siberian Federal University, Kirenskogo, 26, Krasnoyarsk, 660026, Russia
The identification of an unknown constant coefficient in the main term of the partial differential equation $ - kM\psi(u) + g(x) u = f(x) $ with the Dirichlet boundary condition is investigated. Here $\psi(u)$ is a nonlinear increasing function of $u$, $M$ is a linear self-adjoint elliptic operator of the second order. The coefficient $k$ is recovered on the base of additional integral boundary data. The existence and uniqueness of the solution to the inverse problem involving a function $u$ and a positive real number $k$ is proved.
inverse problem, boundary value problem, second-order elliptic equations, existence and uniqueness theorem, filtration.
PDF file (192 kB)
Received in revised form: 03.12.2014
Anna Sh. Lyubanova, “On an inverse problem for quasi-linear elliptic equation”, J. Sib. Fed. Univ. Math. Phys., 8:1 (2015), 38–48
Citation in format AMSBIB
\paper On an inverse problem for quasi-linear elliptic equation
\jour J. Sib. Fed. Univ. Math. Phys.
Citing articles on Google Scholar:
Related articles on Google Scholar:
This publication is cited in the following articles:
A. Sh. Lyubanova, “Obratnye zadachi dlya nelineinykh statsionarnykh uravnenii”, Matematicheskie zametki SVFU, 23:2 (2016), 65–77
Anna Sh. Lyubanova, “The inverse problem for the nonlinear pseudoparabolic equation of filtration type”, Zhurn. SFU. Ser. Matem. i fiz., 10:1 (2017), 4–15
A. Sh. Lyubanova, A. V. Velisevich, “Inverse problems for the stationary and pseudoparabolic equations of diffusion”, Appl. Anal., 98:11 (2019), 1997–2010
|Number of views:|