On the stability of inverse problems

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August undefined, 2024

Web13 de fev. de 2009 · We consider the stability in an inverse problem of determining the potential q entering the wave equation ∂ 2 t u − ∆u + q(x)u = 0 in a bounded smooth … Web1 de set. de 1984 · WAVE MOTION 6 (1984) 489-499 489 NORTH-HOLLAND ON THE STABILITY OF INVERSE SCATTERING PROBLEMS John FAWCETT Department of Mathematics, Stanford University, Stanford, CA 94305, USA Received 26 October 1983 Some aspects of the time-dependent inverse scattering problem are discussed. Then …

On the seismic inverse problem: uniqueness, stability and …

Web15 de jun. de 2024 · The inverse problem may be recast as the optimization problem (5) inf J ( β, γ) subject to ( β, γ) ∈ U a d ( Ω) and ( S, I) a solution of (1)– (4). where the cost … WebOutline 1 Motivation: Re ection Seismology 2 Mathematical model: time harmonic case, linearized elasticity, isotropic medium 3 The inverse problem 4 Some history 5 Regularization: Unknown parameters are piecewise constant on a nite partition of the background domain 6 Parameter identi cation (given the partition) 7 Quantitative … how big is a standard headphone jack

On the stability of the solution of the inverse problem for Dirac ...

Web1 de abr. de 2024 · In the present paper, we study the stability of the solution of the inverse problem for Dirac operator ℓ Q. First, we introduce a Riesz basis consisting of vector-valued eigenfunctions of the problem (1) – (2) in a Hilbert space. Then, some properties of the Green’s matrix of the operator are established. WebIn this paper, we show for the first time the stability of the inverse source problem for the three-dimensional Helmholtz equation in an inhomogeneous background medium. The … WebThe work continues a series of articles devoted to the peculiarities of solving coefficient inverse problems for nonlinear singularly perturbed equations of the reaction-diffusion-advection-type with data on the position of the reaction front. In this paper, we place the emphasis on some problems of the numerical solving process. One of the approaches … how many octaves on a grand piano

Local solvability and stability of the inverse problem for the non …

On the local Lipschitz stability of Bayesian inverse problems

WebCarl Wunsch, in Encyclopedia of Ocean Sciences (Third Edition), 2024. Abstract. Inverse problems and methods in an oceanographic context are almost always ones of statistical estimation theory. They normally involve a combination of a “model” of some form, as well as observational data. The presence of noise in data, and the common issue of sparse … Web30 de dez. de 2010 · Two inverse problems for the Sturm-Liouville operator Ly = s-y″ + q(x)y on the interval [0, fy] are studied. For θ ⩾ 0, there is a mapping F:W θ 2 → l θ B, F(σ) = {s k} ∞ 1, related to the first of these problems, where W ∞ 2 = W ∞ 2 [0, π] is the Sobolev space, σ = ∫ q is a primitive of the potential q, and l θ B is a specially constructed finite … how big is a standard horse stallWebThis article is published in Mathematical Methods in The Applied Sciences.The article was published on 2024-02-08. It has received 2 citation(s) till now. The article focuses on the topic(s): Boundary value problem. how many octets in a subnet mask

"Web11 de jul. de 2024 · We consider the non-self-adjoint Sturm–Liouville operator on a finite interval. The inverse spectral problem is studied, which consists in recovering this operator from its eigenvalues and generalized weight numbers. We prove local solvability and stability of this inverse problem, relying on the method of spectral mappings. Possible … " - On the stability of inverse problems

On the stability of inverse problems

On the stability of the inverse transmission eigenvalue problem …

Web10 de abr. de 2024 · Abstract: This brief paper investigates the stability and L∞-gain of positive fractional-order singular systems (FOSSs) with time-varying delays. Based on the Drazin inverse of singular matrices, an equivalent auxiliary system is developed to avoid the singularity problem, and a sufficient and necessary criterion ensuring the positivity of … Web26 de fev. de 2013 · The coefficient inverse extremal problems are studied for the stationary convectiondiffusion equation in a bounded domain under mixed boundary …

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Web15 de set. de 2024 · Stability of inverse scattering problem. In this section, we study the stability of inverse scattering problem for recovering the potential and the parameter in … Web23 de jun. de 2024 · Download a PDF of the paper titled Uniqueness and stability of an inverse problem for a semi-linear wave equation, by Matti Lassas and 2 other authors …

Web10 de abr. de 2024 · Introduction. This paper is concerned with a nonlinear inverse scattering problem for the Schrödinger equation in two dimensions. Let e i κ x ⋅ d be an incident plane wave with incident direction d ∈ S.Consider the scattering problem modeled by the nonlinear Schrödinger equation in a homogeneous background medium in two … Web16 de jul. de 2024 · [14] Li P, Yuan G and Yuan G 2024 Increasing stability for the inverse source scattering problem with multi-frequencies Inverse Problems Imaging 11 745–59. Go to reference in article Crossref Google Scholar [15] Li P, Zhai J and Zhao Y 2024 Stability for the acoustic inverse source problem in inhomogeneous media SIAM J. …

Web22 de abr. de 2024 · The obtained stability yields under mild assumptions the well-posedness of Bayesian inverse problems, in particular, a well-posedness w.r.t. the … Web10 de abr. de 2024 · Stability for the inverse source problems in elastic and electromagnetic waves. J. Math. Pures Appl., 134 (2024), pp. 122-178. View PDF View …

Web1 de mar. de 2013 · I www.sciencedirect.com artial Differential Equations remark on Lipschitz stability for inverse problems ne remarque sur la stabilitÃ© lipschitzienne pour les problÃ¨mes inverses aurent Bourgeois boratoire POEMS, ENSTA ParisTech, 828, boulevard des MarÃ©chaux, 91762 Palaiseau cedex, France rticle info abstract ticle …

Web1 de jan. de 1993 · Issues of the Journal of Inverse and Ill-Posed Problems contain high quality papers which have an innovative approach and topical interest. The following … how many odd 3 digit numbersWebA. Choudhury and H. Heck, Stability of the inverse boundary value problem for the biharmonic operator: Logarithmic estimates, J. Inverse Ill-Posed Probl., 25 (2024), pp. 251--263. Google Scholar 8. how big is a standard jelly roll panWeb, On certain inverse problems for parabolic equations with final and integral observation, Sb. Math. 75 (2) (1993) 473. Google Scholar [33] Prilepko Aleksey I., Kamynin Vitaly L., Kostin Andrew B., Inverse source problem for parabolic equation with the condition of integral observation in time, J. Inverse Ill-Posed Probl. 26 (4) (2024) 523 – 539. how many octogenarians are in congressWebInverse Problems Lecture notes, Michaelmas term 2024 University of Cambridge Hanne Kekkonen and Yury Korolev ... (Stability) The direct or forward problem is assumed to … how many octet in ip addressWeb15 de set. de 2024 · Stability of direct and inverse scattering problems for the self-adjoint Schrödinger operators on the half-line. Author links open overlay panel Xiao-Chuan Xu. … how many octaves in guitarWebAn inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field.It is called an inverse problem because it starts with … how many odd days are there in 300 yearsWebInverse problems have been encountered in many areas of ap- ... In order to study the stability of the optimization problems (4) and (6) at ! , we will characterize the second … how big is a standard mason jar