Identifiability, stability and reconstruction results of point sources by boundary measurements in heteregeneous trees.

Nicaise, Serge; Zair, Ouahiba

doi:10.5209/rev_rema.2003.v16.n1.16865

Cited by 15 publications

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“…Observing data over spatial sets like (3) in inverse problems is not new. [7,8] In [8] (see also [9, chap.7, sec.2]), the authors analyze the wave equation problem…”

Section: Main Results To Be Provedmentioning

confidence: 99%

Uniqueness results in the identification of distributed sources over Germain–Lagrange plates by boundary measurements

Kawano

2015

Applicable Analysis

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We prove that the loading composed by a finite sum of time-independent sources acting over a bounded plate can be uniquely identified by knowing the normal derivative of the displacement along a subset of the boundary or the displacement of the points in a certain set near the boundary. This is true even if these data correspond to an arbitrary small interval of time. The method used is to reduce the problem to another one for the wave equation. ARTICLE HISTORY

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“…Observing data over spatial sets like (3) in inverse problems is not new. [7,8] In [8] (see also [9, chap.7, sec.2]), the authors analyze the wave equation problem…”

Section: Main Results To Be Provedmentioning

confidence: 99%

Uniqueness results in the identification of distributed sources over Germain–Lagrange plates by boundary measurements

Kawano

2015

Applicable Analysis

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“…It should be also noticed that the analysis of this inverse problem is not only important per se, but it will provide a theoretical foundation to other identification methods, such as the Statistical Energy Method, which are used to locate vibration sources in complex structures by the flow energy balance among their components and by measurements taken on few accessible sites only. For the sake of completeness, we recall that Nicaise and Zaïr have considered in [10] the problem of determining point sources in a mechanical system obtained by the connection of a finite number of taut strings from Neumann boundary observations taken on a part of the boundary of the system. However, the analysis of string-like structures involves second order differential operators in the space variable rather then fourth order as in the case of beams and plates.…”

Section: Introductionmentioning

confidence: 99%

Uniqueness in the determination of loads in multi-span beams and plates

Kawano

Morassi

2018

Eur. J. Appl. Math

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Most of the results available on the inverse problem of determining loads acting on elastic beams or plates under transverse vibration refer to single beam or single plate. In this paper we consider the determination of sources in multi-span systems obtained by connecting either two Euler-Bernoulli elastic beams or two rectangular Kirchhoff-Love elastic plates. The material of the structure is assumed to be homogeneous and isotropic. The transverse load is of the form g(t)f (x), where g(t) is a known function of time and f (x) is the unknown term depending on the position variable x. Under slight a priori assumptions, we prove a uniqueness result for f (x) in terms of observations of the dynamic response taken at interior points of the structure in an arbitrary small interval of time. A numerical implementation of the method is included to show the possible application of the results in the practical identification of the source term.

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“…The wave equation. We start with the so-called identity with multiplier (compare with Lemma 3.1 of [35]) which is the key identity for an observability estimate.…”

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confidence: 99%

Control and stabilization of 2 × 2 hyperbolic systems on graphs

Nicaise¹

2017

Mathematical Control &Amp; Related Fields

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We consider 2 × 2 (first order) hyperbolic systems on networks subject to general transmission conditions and to some dissipative boundary conditions on some external vertices. We find sufficient but natural conditions on these transmission conditions that guarantee the exponential decay of the full system on graphs with dissipative conditions at all except one external vertices. This result is obtained with the help of a perturbation argument and an observability estimate for an associated wave type equation. An exact controllability result is also deduced.

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Identifiability, stability and reconstruction results of point sources by boundary measurements in heteregeneous trees.

Cited by 15 publications

References 0 publications

Uniqueness results in the identification of distributed sources over Germain–Lagrange plates by boundary measurements

Uniqueness results in the identification of distributed sources over Germain–Lagrange plates by boundary measurements

Uniqueness in the determination of loads in multi-span beams and plates

Control and stabilization of 2 × 2 hyperbolic systems on graphs

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