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arXiv · 1306.6026

Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem

Herbert Egger·Jan-Frederik Pietschmann·Matthias Schlottbom
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Abstract

In this work we consider the identifiability of two coefficients $a(u)$ and $c(x)$ in a quasilinear elliptic partial differential equation from observation of the Dirichlet-to-Neumann map. We use a linearization procedure due to Isakov [On uniqueness in inverse problems for semilinear parabolic equations. Archive for Rational Mechanics and Analysis, 1993] and special singular solutions to first determine $a(0)$ and $c(x)$ for $x \in Ω$. Based on this partial result, we are then able to determine $a(u)$ for $u \in \mathbb{R}$ by an adjoint approach.

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Herbert Egger, Jan-Frederik Pietschmann, Matthias Schlottbom. 2013-12-11. Simultaneous identification of diffusion and absorption coefficients in a quasilinear elliptic problem. https://doi.org/10.1088/0266-5611%2F30%2F3%2F035009

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