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 … Web15 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. …

On the stability of inverse scattering problems - ScienceDirect

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 … 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 … during the remainder of the year

Inverse Problems - University of Cambridge

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 … Web29 de out. de 2014 · In this paper, we study the stability of two inverse boundary value problems in an infinite slab with partial data. These problems have been studied by Li and Uhlmann for the case of the Schrodinger equation and by Krupchyk, Lassas and Uhlmann for the case of the magnetic Schrodinger equation. Here we quantify the … Web11 de fev. de 2015 · In this study, we consider reconstruction and stability issues of an inverse nodal problem for a p-Laplacian Schrödinger equation with energy dependent potential. We solve Lipschitz stability of the inverse nodal problem for this p-Laplacian operator. Furthermore, we show that the space of all potential functions q is … cryptocurrency mining coinbase

Stability for an Inverse Source Problem of the Biharmonic Operator ...

On the stability of an inverse problem for the wave equation

Web30 de set. de 2024 · We establish Lipschitz stability properties for a class of inverse problems. In that class, the associated direct problem is formulated by an integral operator Am depending non- linearly on a ... Web9 de fev. de 2024 · Download a PDF of the paper titled Stability for an inverse source problem of the biharmonic operator, by Peijun Li and 2 other authors. Download PDF … cryptocurrency mining btc motherboardWeb16 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. … during the rescue isabel got help from

"Web15 de jun. de 2024 · In this note we discuss the existence and stability of an inverse problem arising from the determination of the reaction coefficients for an SIS model. The … " - On the stability of inverse problems

On the stability of inverse problems

Stability properties of an inverse parabolic problem with unknown ...

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 … 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 …

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Web13 de abr. de 2024 · Next we prove the Lipschitz stability for an inverse problem of determining spatially varying factors of source terms and a coefficient by extra boundary … WebInverse 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 …

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 … 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 …

WebD. Hào, Le Thi Thu Giang, S. Kabanikhin, M. Shishlenin. Mathematics. Journal of Inverse and Ill-posed Problems. 2024. Abstract We introduce the concept of very weak solution to a Cauchy problem for elliptic equations. The Cauchy problem is regularized by a well … Web6 de jun. de 2024 · Inverse problems in potential theory are related to problems of the equilibrium shape of a rotating fluid and to problems in geophysics. The central place in studies of inverse problems in potential theory is occupied by the problems of the existence, uniqueness and stability, and also by creating efficient numerical methods for …

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 …

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 … during the remembering state of listening youWebIn this paper, stability results on the inverse random source scattering problems are shown for the one-dimensional Helmholtz equation in a multi-layered medium, where the source function is driven by a spatial Brownian motion. The statistical properties of the random source including expectation and variance are reconstructed from physically … cryptocurrency mining business codeWebIn this paper, stability results on the inverse random source scattering problems are shown for the one-dimensional Helmholtz equation in a multi-layered medium, where the … cryptocurrency mining cell phoneWeb28 de fev. de 2024 · This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at a subboundary. A uniqueness result is obtained by using the analyticity and the newly established unique continuation principle provided that the … cryptocurrency mining computer for saleWeb13 de abr. de 2024 · Next we prove the Lipschitz stability for an inverse problem of determining spatially varying factors of source terms and a coefficient by extra boundary data and spatial data at intermediate time. cryptocurrency mining business planWeb1 de mar. de 2024 · Concerning the inverse problem of bottom detection through measures on the free surface, in [15], the authors used the simple elliptic formulation (1.4)–(1.3) of … cryptocurrency mining device cryptocurrency mining data center