Geodesic
On an inverse problem for quasi-linear elliptic equation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 1, pp. 38-48

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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
Mots-clés : filtration. 
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     author = {Anna Sh. Lyubanova},
     title = {On an inverse problem for quasi-linear elliptic equation},
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     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2015_8_1_a5/}
}
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Anna Sh. Lyubanova. On an inverse problem for quasi-linear elliptic equation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 8 (2015) no. 1, pp. 38-48. http://geodesic.mathdoc.fr/item/JSFU_2015_8_1_a5/