All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 4 Next

Displaying 61 – 80 of 355

Showing per page

Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress

Victor Isakov, Nanhee Kim (2008)

Applicationes Mathematicae

We derive Carleman type estimates with two large parameters for a general partial differential operator of second order. The weight function is assumed to be pseudo-convex with respect to the operator. We give applications to uniqueness and stability of the continuation of solutions and identification of coefficients for the Lamé system of dynamical elasticity with residual stress. This system is anisotropic and cannot be principally diagonalized, but it can be transformed into an "upper triangular"...

Crack detection using electrostatic measurements

Martin Brühl, Martin Hanke, Michael Pidcock (2001)

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

In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes the practical implementation...

Crack detection using electrostatic measurements

Martin Brühl, Martin Hanke, Michael Pidcock (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we extend recent work on the detection of inclusions using electrostatic measurements to the problem of crack detection in a two-dimensional object. As in the inclusion case our method is based on a factorization of the difference between two Neumann-Dirichlet operators. The factorization possible in the case of cracks is much simpler than that for inclusions and the analysis is greatly simplified. However, the directional information carried by the crack makes the practical...

Determination of a diffusion coefficient in a quasilinear parabolic equation

Fatma Kanca (2017)

Open Mathematics

This paper investigates the inverse problem of finding the time-dependent diffusion coefficient in a quasilinear parabolic equation with the nonlocal boundary and integral overdetermination conditions. Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown. Finally, some numerical experiments are presented.

Determination of the unknown source term in a linear parabolic problem from the measured data at the final time

Müjdat Kaya (2014)

Applications of Mathematics

The problem of determining the source term F ( x , t ) in the linear parabolic equation u t = ( k ( x ) u x ( x , t ) ) x + F ( x , t ) from the measured data at the final time u ( x , T ) = μ ( x ) is formulated. It is proved that the Fréchet derivative of the cost functional J ( F ) = ∥ μ T ( x ) - u ( x , T ) ∥ 0 2 can be formulated via the solution of the adjoint parabolic problem. Lipschitz continuity of the gradient is proved. An existence result for a quasi solution of the considered inverse problem is proved. A monotone iteration scheme is obtained based on the gradient method. Convergence rate is proved....

Currently displaying 61 – 80 of 355