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On the inverse boundary value problem for linear isotropic elasticity
Inverse Problems, 2002The authors derive three results on the inverse problem of determining the Lamé parameters \(\lambda(x)\) and \(\mu(x)\) for an isotropic elastic body from its Dirichlet-to-Neumann map \(\Lambda\). While, as pointed out by the authors, it is not true that the knowledge of \(\Lambda\) is sufficient to determine the functions \(\lambda\), \(\mu ...
Eskin, G., Ralston, J.
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Comment on Calderon's Paper: "On an Inverse Boundary Value Problem"
Mathematics of Computation, 1989Summary: \textit{A. P. Calderón} [Semin. Numer. Anal. Appl. Continuum Physics, 65- 73 (1980; MR 81k:35160)] determined a method to approximate the conductivity \(\sigma\) of a conducting body in \(R^ n\) (for \(n\geq 2)\) based on measurements of boundary data.
Isaacson, David, Isaacson, Eli L.
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Solution of one inverse boundary value problem in aerohydrodynamics
Russian Mathematics, 2007It is well-known that designing the wing section of an airfoil boat, even within the model of an ideal incompressible fluid (IIF), one encounters some mathematical difficulties. The latter are caused by the ill-posedness of the problems and the double connectedness of the flow domain. The inverse problem is solved in [\textit{M. I.
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The inverse boundary-value problem for an airfoil with a suction slot
Journal of Applied Mathematics and Mechanics, 1997Summary: The problem of constructing an airfoil in a flow of an ideal incompressible fluid for a specified velocity distribution on the contour when there is a suction slot in the airfoil is solved. The boundary of the slot is modelled by a segment of an equipotential with the specified velocity distribution on it.
Abzalilov, D. F. +2 more
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Inverse Boundary Value Problems
1999In this book, so far, we have considered only so-called direct boundary value problems where, given a differential equation, its domain, and a boundary condition, we want to determine its solution.
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New Solution to the Inverse Boundary Value Problem of Aerohydrodynamics
Russian Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Global Uniqueness Theorem for an Inverse Boundary Value Problem
The Annals of Mathematics, 1987The authors prove that the single smooth coefficient, \(\gamma\), of the elliptic operator \(L_{\gamma}=\nabla \cdot \gamma \nabla\) in a bounded region \(\Omega \leq {\mathbb{R}}^ n\) (n\(\geq 3)\) can be recovered from the map which sends the boundary values of a \(\gamma\)-harmonic function u \((L_{\gamma}u=0\) in \(\Omega)\) to the boundary values ...
Sylvester, John, Uhlmann, Gunther
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The forward and inverse problems for a fractional boundary value problem
Applicable Analysis, 2017In this paper, the authors study the forward and inverse problems for a fractional boundary value problem with Dirichlet boundary conditions. The existence and uniqueness of solutions for the forward problem is first proved. Then an inverse source problem is considered.
Yaqin Feng +3 more
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On uniqueness for an inverse boundary value problem in electrical prospection
Applied Mathematics and Computation, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Inverse boundary value problems and the Aharonov Bohm effect
Inverse Problems, 2002Summary: We consider the inverse boundary value problem for the Schrödinger equation with electromagnetic or Yang-Mills potentials in multiconnected domains \(\Omega\subset \mathbb{R}^n\), \(n\geq 2\). We prove that if the Dirichlet-to-Neumann operators on \(\partial\Omega\) are gauge equivalent then the corresponding potentials are gauge equivalent ...
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