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Homogenization with uncertain input parameters

Luděk Nechvátal (2010)

Mathematica Bohemica

We homogenize a class of nonlinear differential equations set in highly heterogeneous media. Contrary to the usual approach, the coefficients in the equation characterizing the material properties are supposed to be uncertain functions from a given set of admissible data. The problem with uncertainties is treated by means of the worst scenario method, when we look for a solution which is critical in some sense.

Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds

Mouhamed Moustapha Fall, Fethi Mahmoudi (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Given a domain Ω of m + 1 and a k -dimensional non-degenerate minimal submanifold K of Ω with 1 k m - 1 , we prove the existence of a family of embedded constant mean curvature hypersurfaces in Ω which as their mean curvature tends to infinity concentrate along K and intersecting Ω perpendicularly along their boundaries.

Hysteresis memory preserving operators

Pavel Krejčí (1991)

Applications of Mathematics

The recent development of mathematical methods of investigation of problems with hysteresis has shown that the structure of the hysteresis memory plays a substantial role. In this paper we characterize the hysteresis operators which exhibit a memory effect of the Preisach type (memory preserving operators). We investigate their properties (continuity, invertibility) and we establish some relations between special classes of such operators (Preisach, Ishlinskii and Nemytskii operators). For a general...

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

Serge Nicaise, Ouahiba Zaïr (2003)

Revista Matemática Complutense

We consider the inverse problem of determining point wave sources in heteregeneous trees, extensions of one-dimensional stratified sets. We show that the Neumann boundary observation on a part of the lateral boundary determines uniquely the point sources if the time of observation is large enough. We further establish a conditional stability and give a reconstructing scheme.

Identification of a localized source in an interstellar cloud: an inverse problem

Meri Lisi, Silvia Totaro (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study an inverse problem for photon transport in an interstellar cloud. In particular, we evaluate the position x 0 of a localized source q x = q 0 δ x - x 0 , inside a nebula (for example, a star). We assume that the photon transport phenomenon is one-dimensional. Since a nebula moves slowly in time, the number of photons U inside the cloud changes slowly in time. For this reason, we consider the so-called quasi-static approximation u to the exact solution U . By using semigroup theory, we prove existence and uniqueness...

Identification of a wave equation generated by a string

Amin Boumenir (2014)

ESAIM: Control, Optimisation and Calculus of Variations

We show that we can reconstruct two coefficients of a wave equation by a single boundary measurement of the solution. The identification and reconstruction are based on Krein’s inverse spectral theory for the first coefficient and on the Gelfand−Levitan theory for the second. To do so we use spectral estimation to extract the first spectrum and then interpolation to map the second one. The control of the solution is also studied.

Identification of cracks with non linear impedances

Mohamed Jaoua, Serge Nicaise, Luc Paquet (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider the inverse problem of determining a crack submitted to a non linear impedance law. Identifiability and local Lipschitz stability results are proved for both the crack and the impedance.

Identification of cracks with non linear impedances

Mohamed Jaoua, Serge Nicaise, Luc Paquet (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the inverse problem of determining a crack submitted to a non linear impedance law. Identifiability and local Lipschitz stability results are proved for both the crack and the impedance.

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