On the stability of inverse problems
WebAn 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 … Weband the stability for the inverse source problems. The main purpose of this article is to establish the Lipschitz stability for the above two types of inverse problems, which have not been found in the existing articles. We mainly consider a linearized equation of (1.1), which is formulated as follows. We set ∂i = ∂ ∂xi, 1 ≤ i ≤ d and ...
On the stability of inverse problems
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Web26 de fev. de 2013 · The coefficient inverse extremal problems are studied for the stationary convectiondiffusion equation in a bounded domain under mixed boundary … WebA. 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. …
Web15 de abr. de 2024 · Stability of the inverse spectral problem. In this section, we consider stability of the inverse spectral problems for the problem R (a, q) due to McLaughlin … 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.
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 … Web1 de jan. de 2024 · For the inverse problem, we obtain sufficient conditions for a function to be the S-function of the scattering problem on the forked-shaped graph with zero potential on the half-infinite edge, and ...
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 …
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 … poppy travel perfume bath and body workspoppy trail by metlox made in californiaWeb22 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 … sharing pc to tvWeb10 de mai. de 2024 · We establish a logarithmic stability estimate for the inverse problem of determining the nonlinear term, appearing in a semilinear boundary value problem, from the corresponding Dirichlet-to-Neumann map. Our result can be seen as a stability inequality for an earlier uniqueness result by Isakov and Sylvester (Commun Pure Appl … poppy treffryWeb10 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 … poppytrail by metlox leadWeb1 de jan. de 2007 · Stability estimates for a plate problem were studied in Gao 15 and Wang, 16 the Lipschitz stability for a Kirchhoff plate equation was obtained in Yuan and Yamamoto, 17 and inverse source problems ... poppytrail pottery made in californiaWeb23 de dez. de 2024 · Uniqueness and stability are established for both of the inverse source problems. Based on either continuous or discrete multi-frequency data, a unified … sharing pdf