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Let $Ω$ be a bounded, convex planar domain whose boundary has a not too degenerate curvature. In this paper we provide partial answers to an identification question associated with the boundary value problem $▵ u = - c u - d in Ω, u = 0 on \partial Ω .$ We prove two results: 1) If $Ω$ is not a ball and if one considers only solutions with $- c u - d \leq 0$ , then there exist at most finitely many pairs of coefficients $(c, d)$ so that the normal derivative $\frac{\partial u}{\partial ν} |_{\partial Ω}$ equals a given $ψ \neq 0$ .2) If one imposes no sign condition on the solutions but one additionally supposes that $Ω$ is sufficiently...

An inverse problem for time-harmonic electromagnetic currents in a smoothly layered medium.

Malmivuori, Markku (2005)

Annales Academiae Scientiarum Fennicae. Mathematica

An inverse problem in a parabolic equation.

Li, Zhilin, Zheng, Kewang (1997)

Electronic Journal of Differential Equations (EJDE) [electronic only]

An inverse problem of the wave equation.

J. Sjöstrand, A.G. Ramm (1991)

Mathematische Zeitschrift

An inversion of the obstacle problem and its explicit solution

Hans Lewy (1979)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Anisotropic inverse problems and Carleman estimates

David Dos Santos Ferreira (2007/2008)

Séminaire Équations aux dérivées partielles

This note reports on recent results on the anisotropic Calderón problem obtained in a joint work with Carlos E. Kenig, Mikko Salo and Gunther Uhlmann [8]. The approach is based on the construction of complex geometrical optics solutions to the Schrödinger equation involving phases introduced in the work [12] of Kenig, Sjöstrand and Uhlmann in the isotropic setting. We characterize those manifolds where the construction is possible, and give applications to uniqueness for the corresponding anisotropic...

Application des sentinelles à l'identification des pollutions dans une rivière

B.-E. Ainseba, J.-P. Kernevez, R. Luce (1994)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Application of Rothe's method to a parabolic inverse problem with nonlocal boundary condition

Yong-Hyok Jo, Myong-Hwan Ri (2022)

Applications of Mathematics

We consider an inverse problem for the determination of a purely time-dependent source in a semilinear parabolic equation with a nonlocal boundary condition. An approximation scheme for the solution together with the well-posedness of the problem with the initial value $u_{0} \in H^{1} (Ω)$ is presented by means of the Rothe time-discretization method. Further approximation scheme via Rothe’s method is constructed for the problem when $u_{0} \in L^{2} (Ω)$ and the integral kernel in the nonlocal boundary condition is symmetric.

Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter

Michael S. Vogelius, Darko Volkov (2000)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter

Michael S. Vogelius, Darko Volkov (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider solutions to the time-harmonic Maxwell's Equations of a TE (transverse electric) nature. For such solutions we provide a rigorous derivation of the leading order boundary perturbations resulting from the presence of a finite number of interior inhomogeneities of small diameter. We expect that these formulas will form the basis for very effective computational identification algorithms, aimed at determining information about the inhomogeneities from electromagnetic boundary measurements. ...

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