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On an Inverse Diffusion Problem

SIAM Journal on Applied Mathematics, 1997
Summary: In many applications, such as the heat conduction and hydrology, there is a need to recover the (possibly discontinuous) diffusion coefficient \(a\) from boundary measurements of solutions of a parabolic equation. The complete inverse problem is ill posed and nonlinear, so a numerical solution is quite difficult, and we linearize the problem ...
Alaeddin Elayyan, Victor Isakov
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Type of inversion problem in physics:  An inverse emissivity problem

Physical Review E, 2001
Inversion problems have recently drawn vast amounts of attention from the physics community due to their potential widespread applications. In this Rapid Communication, a different type of inversion problem in physics is proposed: an inverse emissivity problem, which aims to determine the emissivity g(nu) by measuring only the total radiated power J(T).
T, Wen   +4 more
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The Inverse Decay Problem

Journal of Mathematical Physics, 1971
Let UK(t) be a one-parameter operator family of positive type in a Hilbert space K and U(t) its minimal unitary dilation with infinitesimal generator H. If UK(t) is a contractive semigroup, then H is not positive. If in addition UK(t)→0 for t → ∞, then there exists a state φ∈K on which H is not defined.
Horwitz, L. P.   +2 more
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Inverse Problems

Foundations of Science, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON THE INVERSE RESONANCE PROBLEM

Journal of the London Mathematical Society, 2003
A new technique is presented which gives conditions under which perturbations of certain base potentials are uniquely determined from the location of eigenvalues and resonances in the context of a Schrödinger operator on a half-line. In particular, the authors want to treat complex-valued potential as well as potentials with slower or perhaps no decay ...
Brown, B. M., Knowles, I., Weikard, R.
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The Inverse Caustic Problem

The American Mathematical Monthly, 2020
For a family of parallel incoming light rays, we consider the problem of finding a reflecting curve Γ that has as its caustic a given curve γ.
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Inverse problems in ecology

Journal of Theoretical Biology, 1966
Abstract The question of describing interactions of populations is studied. From observations of population growths, parameters in models may be estimated. This concept is illustrated by an example of two interacting species. The sensitivity of the parameters to the accuracy of the observations is computationally investigated, using the technique of ...
R, Bellman, H, Kagiwada, R, Kalaba
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Inverse Problem with Constraints

Physical Review Letters, 1973
A procedure is presented for constructing a solution to the inverse problem subject to the constraint that the wave functions be prescribed at a finite number of energies.
D. J. Ernst   +3 more
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On the inverse conductivity problem

Applied Mathematics and Computation, 1998
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yildiz, B, Sever, A
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Inverse Eigenvalue Problems

SIAM Review, 1998
In the inverse eigenvalue problem, one has to construct a matrix with a (partially) given spectrum. The problem appears in many different forms and in many different applications. Usually the problem is constrained in the sense that the matrix \(M\) that one wants to find has to be in a certain class. For example it should be of the form \(M=A+X\) or \(
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