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On the EIT problem for nonorientable surfaces J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-12-18 M. I. Belishev; D. V. Korikov
Let (Ω,g) be a smooth compact two-dimensional Riemannian manifold with boundary and let Λg:f↦∂νu|∂Ω be its DN map, where u obeys Δgu=0 in Ω and u|∂Ω=f. The Electric Impedance Tomography Problem is to determine Ω from Λg. A criterion is proposed that enables one to detect (via Λg) whether Ω is orientable or not. The algebraic version of the BC-method is applied to solve the EIT problem for the Moebius
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The modulus of the Fourier transform on a sphere determines 3-dimensional convex polytopes J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2021-01-12 Konrad Engel; Bastian Laasch
Let 𝒫 and P′ be 3-dimensional convex polytopes in R3 and S⊆R3 be a non-empty intersection of an open set with a sphere. As a consequence of a somewhat more general result it is proved that 𝒫 and P′ coincide up to translation and/or reflection in a point if |∫Pe-is⋅xdx|=|∫P′e-is⋅xdx| for all s∈S. This can be applied to the field of crystallography regarding the question whether a nanoparticle
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Decentralized and parallel primal and dual accelerated methods for stochastic convex programming problems J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2021-01-22 Darina Dvinskikh; Alexander Gasnikov
We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for all classes of the objective, the optimality in terms of the number of oracle calls per node takes place only up to a logarithmic factor and the notion of smoothness
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A posteriori choice of time-discretization step in finite difference methods for solving ill-posed Cauchy problems in Hilbert space J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2021-01-22 Mikhail M. Kokurin
Finite difference semidiscretization methods for solving an ill-posed Cauchy problem in a Hilbert space are investigated. The problems involve linear positively definite selfadjoint operators. We justify an a posteriori scheme for the choice of the time-discretization step and establish accuracy estimates in terms of the error level of input data.
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Recovery of the time-dependent implied volatility of time fractional Black–Scholes equation using linearization technique J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2021-01-22 Sajad Iqbal; Yujie Wei
This paper tries to examine the recovery of the time-dependent implied volatility coefficient from market prices of options for the time fractional Black–Scholes equation (TFBSM) with double barriers option. We apply the linearization technique and transform the direct problem into an inverse source problem. Resultantly, we get a Volterra integral equation for the unknown linear functional, which is
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Inverse problems in analysis of input-output model in the class of CES functions J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2021-01-15 Alexander A. Shananin; Anastasiya V. Rassokha
The article proposes a modification of the approach to the analysis of inter-industry balance. Instead of linear models of inter-industry balance, based on the hypothesis of W. Leontief about the constancy of the cost standards of production factors, the article studies nonlinear models. For the case of production functions with constant elasticity of substitution (CES) an algorithm for solving the
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Possibilities for separation of scalar and vector characteristics of acoustic scatterer in tomographic polychromatic regime J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2021-01-16 Olga D. Rumyantseva; Andrey S. Shurup; Dmitriy I. Zotov
The inverse wave problem of tomographic type is considered. It consists in reconstruction of several scatterer’s characteristics in the form of spatial distributions for sound speed, medium density, absorption coefficient and power index of its frequency dependence, as well as vector of flow velocity. In the form of a survey material (based on several publications), a sequence of steps is discussed
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Guided image filtering based ℓ0 gradient minimization for limited-angle CT image reconstruction J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2021-01-14 Tianyi Wang; Chengxiang Wang; Kequan Zhao; Wei Yu; Min Huang
Limited-angle computed tomography (CT) reconstruction problem arises in some practical applications due to restrictions in the scanning environment or CT imaging device. Some artifacts will be presented in image reconstructed by conventional analytical algorithms. Although some regularization strategies have been proposed to suppress the artifacts, such as total variation (TV) minimization, there is
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On the convergence of recursive SURE for total variation minimization J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2021-01-09 Feng Xue; Xia Ai; Jiaqi Liu
Recently, total variation (TV) regularization has become a standard technique for image recovery. The mean squared error (MSE) of the reconstruction can be reliably estimated by Stein’s unbiased risk estimate (SURE). In this work, we develop two recursive evaluations of SURE, based on Chambolle’s projection method (CPM) for TV denoising and alternating direction method of multipliers (ADMM) for TV
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Joint inversion of high-frequency induction and lateral logging sounding data in earth models with tilted principal axes of the electrical resistivity tensor J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2021-01-08 Oleg Nechaev; Viacheslav Glinskikh; Igor Mikhaylov; Ilya Moskaev
In this article, we are the first to formulate the direct and inverse problems of resistivity logging on determining the components of the electrical resistivity tensor of rocks from a set of high-frequency induction and lateral logging sounding measurements. Using a finite element approximation, high-order hierarchical basis functions, computationally efficient multilevel methods and a multistart
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Nonlinear dynamics of pulsating detonation wave with two-stage chemical kinetics in the shock-attached frame J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-12-22 Yaroslava E. Poroshyna; Aleksander I. Lopato; Pavel S. Utkin
The paper contributes to the clarification of the mechanism of one-dimensional pulsating detonation wave propagation for the transition regime with two-scale pulsations. For this purpose, a novel numerical algorithm has been developed for the numerical investigation of the gaseous pulsating detonation wave using the two-stage model of kinetics of chemical reactions in the shock-attached frame. The
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Ambarzumyan-type theorem for the impulsive Sturm–Liouville operator J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-12-19 Ran Zhang; Chuan-Fu Yang
We prove that if the Neumann eigenvalues of the impulsive Sturm–Liouville operator -D2+q in L2(0,π) coincide with those of the Neumann Laplacian, then q=0.
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Convexity of a discrete Carleman weighted objective functional in an inverse medium scattering problem J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-12-17 Nguyen Trung Thành
We investigate a globally convergent method for solving a one-dimensional inverse medium scattering problem using backscattering data at a finite number of frequencies. The proposed method is based on the minimization of a discrete Carleman weighted objective functional. The global convexity of this objective functional is proved.
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Conditional stability in a backward Cahn–Hilliard equation via a Carleman estimate J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-12-16 Yunxia Shang; Shumin Li
We consider a Cahn–Hilliard equation in a bounded domain Ω in ℝn over a time interval (0,T) and discuss the backward problem in time of determining intermediate data u(x,θ), θ∈(0,T), x∈Ω from the measurement of the final data u(x,T), x∈Ω. Under suitable a priori boundness assumptions on the solutions u(x,t), we prove a conditional stability estimate for the semilinear Cahn–Hilliard equation
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Inverse problem of shape identification from boundary measurement for Stokes equations: Shape differentiability of Lagrangian J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-12-16 Victor A. Kovtunenko; Kohji Ohtsuka
For Stokes equations under divergence-free and mixed boundary conditions, the inverse problem of shape identification from boundary measurement is investigated. Taking the least-square misfit as an objective function, the state-constrained optimization is treated by using an adjoint state within the Lagrange approach. The directional differentiability of a Lagrangian function with respect to shape
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Stability estimates for reconstruction from the Fourier transform on the ball J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-12-11 Mikhail Isaev; Roman G. Novikov
We prove Hölder-logarithmic stability estimates for the problem of finding an integrable function v on ℝd with a super-exponential decay at infinity from its Fourier transform ℱv given on the ball Br. These estimates arise from a Hölder-stable extrapolation of ℱv from Br to a larger ball. We also present instability examples showing an optimality of our results.
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Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-12-02 Leonid L. Frumin
We introduce numerical algorithms for solving the inverse and direct scattering problems for the Manakov model of vector nonlinear Schrödinger equation. We have found an algebraic group of 4-block matrices with off-diagonal blocks consisting of special vector-like matrices for generalizing the scalar problem’s efficient numerical algorithms to the vector case. The inversion of block matrices of the
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Imaging of bi-anisotropic periodic structures from electromagnetic near-field data J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-24 Dinh-Liem Nguyen; Trung Truong
This paper is concerned with the inverse scattering problem for the three-dimensional Maxwell equations in bi-anisotropic periodic structures. The inverse scattering problem aims to determine the shape of bi-anisotropic periodic scatterers from electromagnetic near-field data at a fixed frequency. The factorization method is studied as an analytical and numerical tool for solving the inverse problem
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Retraction of: Convergence of a series associated with the convexification method for coefficient inverse problems J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-27 Michael V. Klibanov; Dinh-Liem Nguyen
Journal Name: Journal of Inverse and Ill-posed Problems Volume: -1 Issue: ahead-of-print
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Modeling and simulation of Compton scatter image formation in positron emission tomography J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-09 Ivan G. Kazantsev; Samuel Matej; Robert M. Lewitt; Ulrik L. Olsen; Henning F. Poulsen; Ivan P. Yarovenko; Igor V. Prokhorov
We present the comparative study of the analytical forward model and the statistical simulation of the Compton single scatter in the positron emission tomography. The formula of the forward model has been obtained using the single scatter simulation approximation under simplified assumptions, and therefore we calculate scatter projections using independent Monte Carlo simulation mimicking the scatter
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Correlation of errors in inverse problems of optical coatings monitoring J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-25 Igor V. Kochikov; Svetlana A. Sharapova; Anatoly G. Yagola; Alexander V. Tikhonravov
On-line optical monitoring of multilayer coating production requires solving inverse identification problems of determining the thicknesses of coating layers. Regardless of the algorithm used to solve inverse problems, the errors in the thicknesses of the deposited layers are correlated by the monitoring procedure. Studying the correlation of thickness errors is important for the production of the
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Frontmatter J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-12-01
Journal Name: Journal of Inverse and Ill-posed Problems Volume: 28 Issue: 6 Pages: i-iv
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A perturbation analysis based on group sparse representation with orthogonal matching pursuit J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-17 Chunyan Liu; Feng Zhang; Wei Qiu; Chuan Li; Zhenbei Leng
In this paper, by exploiting orthogonal projection matrix and block Schur complement, we extend the study to a complete perturbation model. Based on the block-restricted isometry property (BRIP), we establish some sufficient conditions for recovering the support of the block 𝐾-sparse signals via block orthogonal matching pursuit (BOMP) algorithm. Under some constraints on the minimum magnitude of
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Global stability result for parabolic Cauchy problems J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-19 Mourad Choulli; Masahiro Yamamoto
Uniqueness of parabolic Cauchy problems is nowadays a classical problem and since Hadamard [Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Dover, New York, 1953], these kind of problems are known to be ill-posed and even severely ill-posed. Until now, there are only few partial results concerning the quantification of the stability of parabolic Cauchy problems. We bring in the
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Inverse extremum problem for a model of endovenous laser ablation J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-19 Andrey Kovtanyuk; Alexander Chebotarev; Alena Astrakhantseva
An inverse extremum problem (optimal control problem) for a quasi-linear radiative-conductive heat transfer model of endovenous laser ablation is considered. The problem is to find the powers of the source spending on heating the fiber tip and on radiation. As a result, it provides a given temperature distribution in some part of the model domain. The unique solvability of the initial-boundary value
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Machine learning based data retrieval for inverse scattering problems with incomplete data J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-19 Yu Gao; Kai Zhang
We are concerned with the inverse scattering problems associated with incomplete measurement data. It is a challenging topic of increasing importance that arise in many practical applications. Based on a prototypical working model, we propose a machine learning based inverse scattering scheme, which integrates a CNN (convolution neural network) for the data retrieval. The proposed method can effectively
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Direct and inverse scalar scattering problems for the Helmholtz equation in ℝm J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-19 Yury G. Smirnov; Aleksei A. Tsupak
The boundary value problem for the Helmholtz equation in the m-dimensional free space is considered. The problem is reduced to the Lippmann–Schwinger integral equation over the inhomogeneity domain. The operator of the integral equation is shown to be an invertible Fredholm operator. The inverse coefficient problem is considered. An application of the two-step method reduces the inverse problem to
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Inverse problem for a degenerate/singular parabolic system with Neumann boundary conditions J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-18 Mohammed Alaoui; Abdelkarim Hajjaj; Lahcen Maniar; Jawad Salhi
In this paper, we study an inverse source problem for a degenerate and singular parabolic system where the boundary conditions are of Neumann type. We consider a problem with degenerate diffusion coefficients and singular lower-order terms, both vanishing at an interior point of the space domain. In particular, we address the question of well-posedness of the problem, and then we prove a stability
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On local and global structures of transmission eigenfunctions and beyond J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-07 Hongyu Liu
The (interior) transmission eigenvalue problems are a type of non-elliptic, non-selfadjoint and nonlinear spectral problems that arise in the theory of wave scattering. They connect to the direct and inverse scattering problems in many aspects in a delicate way. The properties of the transmission eigenvalues have been extensively and intensively studied over the years, whereas the intrinsic properties
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Inverting the variable fractional order in a variable-order space-fractional diffusion equation with variable diffusivity: analysis and simulation J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-10 Xiangcheng Zheng; Yiqun Li; Jin Cheng; Hong Wang
Variable-order space-fractional diffusion equations provide very competitive modeling capabilities of challenging phenomena, including anomalously superdiffusive transport of solutes in heterogeneous porous media, long-range spatial interactions and other applications, as well as eliminating the nonphysical boundary layers of the solutions to their constant-order analogues. In this paper, we prove
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Inverse problem with final overdetermination for time-fractional differential equation in a Banach space J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-13 Dmitry Orlovsky; Sergey Piskarev
We consider in a Banach space E the inverse problem
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Stability and the inverse gravimetry problem with minimal data J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-11 Victor Isakov; Aseel Titi
The inverse problem in gravimetry is to find a domain 𝐷 inside the reference domain Ω from boundary measurements of gravitational force outside Ω. We found that about five parameters of the unknown 𝐷 can be stably determined given data noise in practical situations. An ellipse is uniquely determined by five parameters. We prove uniqueness and stability of recovering an ellipse for the inverse problem
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Variational-hemivariational inverse problem for electro-elastic unilateral frictional contact problem J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-07 Othmane Baiz; Hicham Benaissa; Zakaria Faiz; Driss El Moutawakil
In the present paper, we study inverse problems for a class of nonlinear hemivariational inequalities. We prove the existence and uniqueness of a solution to inverse problems. Finally, we introduce an inverse problem for an electro-elastic frictional contact problem to illustrate our results.
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Simultaneous identification and reconstruction of the space-dependent reaction coefficient and source term J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-07 Kai Cao; Daniel Lesnic
The inverse problem of simultaneously determining, i.e., identifying and reconstructing, the space-dependent reaction coefficient and source term component from time-integral temperature measurements is investigated. This corresponds to thermal applications in which the heat is generated from a source depending linearly on the temperature, but with unknown space-dependent coefficients. For the resulting
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Mathematical modelling of plasmonic strain sensors J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-07 Habib Ammari; Pierre Millien; Alice L. Vanel
We provide a mathematical analysis for a metasurface constructed of plasmonic nanoparticles mounted periodically on the surface of a microcapsule. We derive an effective transmission condition, which exhibits resonances depending on the inter-particle distance. When the microcapsule is deformed, the resonances are shifted. We fully characterize the dependence of these resonances on the deformation
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The Sommerfeld problem and inverse problem for the Helmholtz equation J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-11-07 T. S. Kalmenov; S. I. Kabanikhin; Aidana Les
The study of a time-periodic solution of the multidimensional wave equation ∂2∂t2u~-Δxu~=f~(x,t), u~(x,t)=eiktu(x), over the whole space ℝ3 leads to the condition of the Sommerfeld radiation at infinity. This is a problem that describes the motion of scattering stationary waves from a source that is in a bounded area. The inverse problem of finding this source is equivalent to reducing the
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Differential evolution algorithm of solving an inverse problem for the spatial Solow mathematical model J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-04 Sergey Kabanikhin; Olga Krivorotko; Zholaman Bektemessov; Maktagali Bektemessov; Shuhua Zhang
The differential evolution algorithm is applied to solve the optimization problem to reconstruct the production function (inverse problem) for the spatial Solow mathematical model using additional measurements of the gross domestic product for the fixed points. Since the inverse problem is ill-posed the regularized differential evolution is applied. For getting the optimized solution of the inverse
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Regularization of a continuation problem for electrodynamic equations J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-15 Vladimir G. Romanov
The problem of continuation of a solution of electrodynamic equations from the time-like half-plane S={x∈R3∣x3=0} inside the half-space R+3={x∈R3∣x3>0} is considered. A regularization method for a solution of this problem with approximate data is proposed, and the convergence of this method for the class of functions that are analytic with respect to space variables is stated.
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Microwave thermometry with potential application in non-invasive monitoring of hyperthermia J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-07 Morteza Ghaderi Aram; Larisa Beilina; Hana Dobsicek Trefna
Integration of an adaptive finite element method (AFEM) with a conventional least squares method has been presented. As a 3D full-wave forward solver, CST Microwave Studio has been used to model and extract both electric field distribution in the region of interest (ROI) and S-parameters of a circular array consisting of 16 monopole antennas. The data has then been fed into a differential inversion
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The inverse problem of recovering the coefficients of a differential equations on a graph J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-04 Victor Sadovnichii; Yaudat Talgatovich Sultanaev; Azamat Akhtyamov
We consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the
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On the clustering of stationary points of Tikhonov’s functional for conditionally well-posed inverse problems J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-09 Mikhail Y. Kokurin
In a Hilbert space, we consider a class of conditionally well-posed inverse problems for which the Hölder type estimate of conditional stability on a bounded closed and convex subset holds. We investigate a finite-dimensional version of Tikhonov’s scheme in which the discretized Tikhonov’s functional is minimized over the finite-dimensional section of the set of conditional stability. For this optimization
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Solving a 1-D inverse medium scattering problem using a new multi-frequency globally strictly convex objective functional J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-11 Nguyen T. Thành; Michael V. Klibanov
We propose a new approach to constructing globally strictly convex objective functional in a 1-D inverse medium scattering problem using multi-frequency backscattering data. The global convexity of the proposed objective functional is proved. We also prove the global convergence of the gradient projection algorithm and derive an error estimate. Numerical examples are presented to illustrate the performance
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Source recovery with a posteriori error estimates in linear partial differential equations J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-17 Alexander S. Leonov
We consider inverse problems of recovering a source term in initial boundary value problems for linear multidimensional partial differential equations (PDEs) of a general form. A universal stable method suitable for solving such inverse problems is proposed. The method allows one to obtain in the same way approximations to exact sources in different kinds of PDEs using various types of linear supplementary
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Regularization of backward time-fractional parabolic equations by Sobolev-type equations J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-03 Dinh Nho Hào; Nguyen Van Duc; Nguyen Van Thang; Nguyen Trung Thành
The problem of determining the initial condition from noisy final observations in time-fractional parabolic equations is considered. This problem is well known to be ill-posed, and it is regularized by backward Sobolev-type equations. Error estimates of Hölder type are obtained with a priori and a posteriori regularization parameter choice rules. The proposed regularization method results in a stable
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Inverse problem of determining an order of the Caputo time-fractional derivative for a subdiffusion equation J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-01 Shavkat Alimov; Ravshan Ashurov
An inverse problem for determining the order of the Caputo time-fractional derivative in a subdiffusion equation with an arbitrary positive self-adjoint operator A with discrete spectrum is considered. By the Fourier method it is proved that the value of ∥Au(t)∥, where u(t) is the solution of the forward problem, at a fixed time instance recovers uniquely the order of derivative. A list of examples
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Some features of solving an inverse backward problem for a generalized Burgers’ equation J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-25 Dmitry V. Lukyanenko; Igor V. Prigorniy; Maxim A. Shishlenin
In this paper, we consider an inverse backward problem for a nonlinear singularly perturbed parabolic equation of the Burgers’ type. We demonstrate how a method of asymptotic analysis of the direct problem allows developing a rather simple algorithm for solving the inverse problem in comparison with minimization of the cost functional. Numerical experiments demonstrate the effectiveness of this approach
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Asymptotic solution of the inverse problem for restoring the modular type source in Burgers’ equation with modular advection J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-01 Nikolay Nikolaevich Nefedov; V. T. Volkov
For a singularly perturbed Burgers’ type equation with modular advection that has a time-periodic solution with an internal transition layer, asymptotic analysis is applied to solve the inverse problem for restoring the function of the source using known information about the observed solution of a direct problem at a given time interval (period).
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In celebration of the 75th birthday of Professor Anatoly Yagola J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-30
Journal Name: Journal of Inverse and Ill-posed Problems Volume: 28 Issue: 5 Pages: 617-619
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Frontmatter J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-01
Journal Name: Journal of Inverse and Ill-posed Problems Volume: 28 Issue: 5 Pages: i-iv
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The fluid-solid interaction scattering problem with unknown buried objects J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-24 Jianli Xiang; Guozheng Yan
Consider the direct and inverse scattering problem of time harmonic acoustic waves by a two-dimensional elastic obstacle which contains an unknown impenetrable object inside. We apply the boundary integral equation method to solve the direct scattering problem. Since the obtained boundary integral system is a mixed form of scalar and vector equations, we consider the existence of the solution in the
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Convexity properties of the normalized Steklov zeta function of a planar domain J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-26 Alexandre Jollivet
We consider the zeta function ζΩ for the Dirichlet-to-Neumann operator of a simply connected planar domain Ω bounded by a smooth closed curve of perimeter 2π. We name the difference ζΩ-ζD the normalized Steklov zeta function of the domain Ω, where 𝔻 denotes the closed unit disk. We prove that (ζΩ-ζD)′′(0)≥0 with equality if and only if Ω is a disk. We also provide an elementary proof that, for a
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Inverse source problem for the abstract fractional differential equation J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-29 Andrey B. Kostin; Sergey I. Piskarev
In a Banach space, the inverse source problem for a fractional differential equation with Caputo–Dzhrbashyan derivative is considered. The initial and observation conditions are given by elements from D(A), and the operator function on the right side is sufficiently smooth. Two types of the observation operator are considered: integral and at the final point. Under the assumptions that operator 𝐴
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A class of inverse problems for fractional order degenerate evolution equations J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-13 Vladimir E. Fedorov; Anna V. Nagumanova; Marko Kostić
The criteria of the well-posedness is obtained for an inverse problem to a class of fractional order in the sense of Caputo degenerate evolution equations with a relatively bounded pair of operators and with the generalized Showalter–Sidorov initial conditions. It is formulated in terms of the relative spectrum of the pair and of the characteristic function of the problem. Sufficient conditions of
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Identification of a space- and time-dependent source in a variable coefficient advection-diffusion equation from Dirichlet and Neumann boundary measured outputs J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-09 Cristiana Sebu
This paper considers the inverse problem of identifying an unknown space- and time-dependent source function F(x,t) in the variable coefficient advection-diffusion equation
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Finite-dimensional iteratively regularized processes with an a posteriori stopping for solving irregular nonlinear operator equations J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-09 Mikhail Y. Kokurin; Alexander I. Kozlov
We construct and study a class of numerically implementable iteratively regularized Gauss–Newton type methods for approximate solution of irregular nonlinear operator equations in Hilbert space. The methods include a general finite-dimensional approximation for equations under consideration and cover the projection, collocation and quadrature discretization schemes. Using an a posteriori stopping rule
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Variation method solving of the inverse problems for Schrödinger-type equation J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-08 Arif Mir Calal Pashaev; Asaf Dashdamir Iskenderov; Qabil Yavar Yaqubov; Matanet Asaf Musaeva
A variation method for solving the inverse problems of determining of the complex quantum potential in a nonlinear non-stationary Schrödinger-type equation with final and boundary observations is considered. The existence and uniqueness theorem of the solution of the variation formulation of the inverse problem is proved, the continuity and continuous differentiability of the quality criterion are
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A partial inverse problem for quantum graphs with a loop J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-10-08 Sheng-Yu Guan; Chuan-Fu Yang; Dong-Jie Wu
We consider the Sturm–Liouville operator on quantum graphs with a loop with the standard matching conditions in the internal vertex and the jump conditions at the boundary vertex. Given the potential on the loop, we try to recover the potential on the boundary edge from the subspectrum. The uniqueness theorem and a constructive algorithm for the solution of this partial inverse problem are provided
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Recovering a time-dependent potential function in a multi-term time fractional diffusion equation by using a nonlinear condition J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-29 Su Zhen Jiang; Yu Jiang Wu
In the present paper, we devote our effort to a nonlinear inverse problem for recovering a time-dependent potential term in a multi-term time fractional diffusion equation from an additional measurement in the form of an integral over the space domain. First we study the existence, uniqueness, regularity and stability of the solution for the direct problem by using the fixed point theorem. And we obtain
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Stable numerical methods for determination of the molecular clusters force fields J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-15 Gulnara M. Kuramshina; Alexander A. Zakharov
The inverse problem of molecular force fields calculation is considered within the theory of regularization. In our strategy, we choose the stabilizing matrix F0 as a result of quantum mechanical calculations. The solution of the inverse problem is finding a matrix 𝐹 which is the nearest by the chosen Euclidean norm to the given ab initio F0. The optimized solution is referred to as regularized quantum
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Inverse source problem for a generalized Korteweg–de Vries equation J. Inverse Ill posed Probl. (IF 0.926) Pub Date : 2020-09-09 Anbu Arivazhagan; Kumarasamy Sakthivel; Natesan Barani Balan
In this paper, we consider a seventh-order generalized Korteweg–de Vries (GKdV) equation and study the boundary stability results concerning the inverse problem of recovering a space-dependent source term. We establish a new boundary Carleman estimate for the seventh-order linear operator with the Dirichlet–Neumann type boundary conditions. Using this crucial estimate along with regularity result of