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Journal of Siberian Federal University. Mathematics & Physics, 2015, Volume 8, Issue 1, Pages 38–48
(Mi jsfu404)
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This article is cited in 5 scientific papers (total 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.
Received: 12.11.2014 Received in revised form: 03.12.2014 Accepted: 20.12.2014
Citation:
Anna Sh. Lyubanova, “On an inverse problem for quasi-linear elliptic equation”, J. Sib. Fed. Univ. Math. Phys., 8:1 (2015), 38–48
Linking options:
https://www.mathnet.ru/eng/jsfu404 https://www.mathnet.ru/eng/jsfu/v8/i1/p38
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