This article is cited in 5 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

Abstract: 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.

Keywords: inverse problem, boundary value problem, second-order elliptic equations, existence and uniqueness theorem, filtration.

UDC: 517.95

Received: 12.11.2014
Received in revised form: 03.12.2014
Accepted: 20.12.2014

Language: English