Elastic parameters of a laminar mass

Feofanova, V. A.; Yakhno, V. G.

doi:10.1007/bf02499444

Cited by 2 publications

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“…In this case, the one-dimensional inverse problem consists of finding ( 3 ) and the Lame functions ( 3 ) and ( 3 ) as functions of one variable 3 with piecewise constant values. The computation of solutions of this type of one-dimensional inverse problems has been studied in [186,187,220]. The modern theory and methods of the construction of solutions of one-dimensional inverse problems for the equations of elastodynamics in elastic composite media can be found in the works [142,214,[224][225][226][227][228].…”

Section: One-dimensional Inverse Dynamicmentioning

confidence: 99%

A Survey on Inverse Problems for Applied Sciences

Yaman

Yakhno²,

Potthast³

2013

Mathematical Problems in Engineering

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The aim of this paper is to introduce inversion-based engineering applications and to investigate some of the important ones from mathematical point of view. To do this we employ acoustic, electromagnetic, and elastic waves for presenting different types of inverse problems. More specifically, we first study location, shape, and boundary parameter reconstruction algorithms for the inaccessible targets in acoustics. The inverse problems for the time-dependent differential equations of isotropic and anisotropic elasticity are reviewed in the following section of the paper. These problems were the objects of the study by many authors in the last several decades. The physical interpretations for almost all of these problems are given, and the geophysical applications for some of them are described. In our last section, an introduction with many links into the literature is given for modern algorithms which combine techniques from classical inverse problems with stochastic tools into ensemble methods both for data assimilation as well as for forecasting.

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