Uniqueness result for inverse problem of geophysics: I

1990 ◽  
Vol 6 (4) ◽  
pp. 635-641 ◽  
Author(s):  
A G Ramm
Keyword(s):  
Inverse Problem ◽  
Uniqueness Result

On the identification of a single body immersed in a Navier-Stokes fluid

2007 ◽  
Vol 18 (1) ◽  
pp. 57-80 ◽  
Author(s):  
A. DOUBOVA ◽  
E. FERNÁNDEZ-CARA ◽  
J. H. ORTEGA
Keyword(s):  
Inverse Problem ◽  
Rigid Body ◽  
Stokes Equations ◽  
Outer Boundary ◽  
Unique Continuation ◽  
Uniqueness Result ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Friction Forces ◽  
Regularity Results

In this work we consider the inverse problem of the identification of a single rigid body immersed in a fluid governed by the stationary Navier-Stokes equations. It is assumed that friction forces are known on a part of the outer boundary. We first prove a uniqueness result. Then, we establish a formula for the observed friction forces, at first order, in terms of the deformation of the rigid body. In some particular situations, this provides a strategy that could be used to compute approximations to the solution of the inverse problem. In the proofs we use unique continuation and regularity results for the Navier-Stokes equations and domain variation techniques.

scholarly journals Inverse Problem Related to Boundary Shape Identification for a Hyperbolic Differential Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Fagueye Ndiaye ◽  
Idrissa Ly
Keyword(s):  
Inverse Problem ◽  
Dirichlet Boundary ◽  
Hyperbolic Equations ◽  
Normal Derivative ◽  
Uniqueness Result ◽  
Lipschitz Stability ◽  
Shape Identification ◽  
Boundary Part ◽  
Principle Theory

In this paper, we are interested in the inverse problem of the determination of the unknown part ∂ Ω , Γ 0 of the boundary of a uniformly Lipschitzian domain Ω included in ℝ N from the measurement of the normal derivative ∂ n v on suitable part Γ 0 of its boundary, where v is the solution of the wave equation ∂ t t v x , t − Δ v x , t + p x v x = 0 in Ω × 0 , T and given Dirichlet boundary data. We use shape optimization tools to retrieve the boundary part Γ of ∂ Ω . From necessary conditions, we estimate a Lagrange multiplier k Ω which appears by derivation with respect to the domain. By maximum principle theory for hyperbolic equations and under geometrical assumptions, we prove a uniqueness result of our inverse problem. The Lipschitz stability is established by increasing of the energy of the system. Some numerical simulations are made to illustrate the optimal shape.

scholarly journals Uniqueness result for inverse problem of geophysics II

1990 ◽  
Vol 3 (3) ◽  
pp. 103-105 ◽  
Author(s):  
A.G. Ramm ◽  
G.Q. Xie
Keyword(s):  
Inverse Problem ◽  
Uniqueness Result

Recovery of non-smooth radiative coefficient from nonlocal observation by diffusion system

2020 ◽  
Vol 28 (3) ◽  
pp. 389-410
Author(s):  
Mengmeng Zhang ◽  
Jijun Liu
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Nonlinear Operator ◽  
Uniqueness Result ◽  
Composite Medium ◽  
Nonlinear Operator Equation ◽  
Time Interval ◽  
Nonlinear Inverse Problem ◽  
Penalty Term ◽  
Heat Conduction Process

AbstractThe heat conduction process in composite medium can be modeled by a parabolic equation with discontinuous radiative coefficient. To detect the composite medium characterized by such a non-smooth coefficient from measurable information about the heat distribution, we consider a nonlinear inverse problem for parabolic equation, with the average measurement of temperature field in some time interval as the inversion input. We firstly establish the uniqueness for this nonlinear inverse problem, based on the property of the direct problem and the known uniqueness result for linear inverse source problem. To solve the inverse problem from a nonlinear operator equation, the differentiability and the tangential condition of this nonlinear map is analyzed. An iterative process called two-point gradient method is proposed by minimizing data-fit term and the penalty term alternatively, with rigorous convergence analysis in terms of the tangential condition. Numerical simulations are presented to illustrate the effectiveness of the proposed method.

scholarly journals Existence and uniqueness results for an inverse problem for a semilinear equation with final overdetermination

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 847-858 ◽  
Author(s):  
Ali Sazaklioglu ◽  
Abdullah Erdogan ◽  
Allaberen Ashyralyev
Keyword(s):  
Banach Space ◽  
Inverse Problem ◽  
Difference Scheme ◽  
Existence And Uniqueness ◽  
Uniqueness Result ◽  
Order Of Accuracy ◽  
First Order ◽  
Existence And Uniqueness Results ◽  
Semilinear Equation ◽  
Uniqueness Results

In the present paper, unique solvability of a source identification inverse problem for a semilinear equation with a final overdetermination in a Banach space is investigated. Moreover, the first order of accuracy Rothe difference scheme is presented for numerically solving this problem. The existence and uniqueness result for this difference scheme is given. The efficiency of the proposed method is evaluated by means of computational experiments.

A uniqueness result for differential pencils with discontinuities from interior spectral data

Analysis ◽  
2019 ◽  
Vol 38 (4) ◽  
pp. 195-202
Author(s):  
Yasser Khalili ◽  
Dumitru Baleanu
Keyword(s):  
Inverse Problem ◽  
Spectral Data ◽  
Uniqueness Result ◽  
Half Line ◽  
Internal Point ◽  
Diffusion Operator ◽  
Differential Pencils

Abstract In this work, the interior spectral data is employed to study the inverse problem for a differential pencil with a discontinuity on the half line. By using a set of values of the eigenfunctions at some internal point and eigenvalues, we obtain the functions {q_{0}(x)} and {q_{1}(x)} applied in the diffusion operator.

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