On the stability of inverse problems
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 … 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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Web1 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 … 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 …
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 … Web13 de fev. de 2009 · Consider the inverse problem of determining the potential q from the Neumann to Dirichlet map Λ q of the wave equation u tt − Δu + qu = 0 in Ω × (0, T) with u(x, 0) = u t (x, 0) = 0.In this paper, a nearly Lipschitz-type stability estimate is established for the inverse problem: for any small > 0, there exists β 0 > 0 such that when for some β > …
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 … WebStability results for inverse problems on manifolds. Desde 20-04-2024 Hasta 20-04-2024. Plaza de las Ciencias, 3, Madrid, España. Organizado por el Instituto de Matemática …
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 …
WebInverse Problems Lecture notes, Michaelmas term 2024 University of Cambridge Hanne Kekkonen and Yury Korolev ... (Stability) The direct or forward problem is assumed to … diabetic nerve leg pain reducerWebThis 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. cinebench temps acer aspire 7Web29 de set. de 2005 · We treat the stability issue for an inverse problem arising from non-destructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem. We obtain that when the unknown part of the … cinebench versionsWeb10 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 … cinebench timespyWeb16 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. … diabetic nerve eye damage symptomsWeb1 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 ... diabetic nerve pain foot reliefWebHowever, the connection between the inverse problem for the RTE and the inverse problem for the elliptic equation has not been fully developed. This problem is particularly interesting because the former one is mildly ill-posed, with a Lipschitz type stability estimate, while the latter is well known to be severely ill-posed with a logarithmic type … cinebench which version