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The BC-method in Multidimensional Spectral Inverse Problem: Theory and Numerical Illustrations

M. I. Belishev, V. Yu. Gotlib, S. A. Ivanov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This work is devoted to numerical experiments for multidimensional Spectral Inverse Problems. We check the efficiency of the algorithm based on the BC-method, which exploits relations between Boundary Control Theory and Inverse Problems. As a test, the problem for an ellipse is considered. This case is of interest due to the fact that a field of normal geodesics loses regularity on a nontrivial separation set. The main result is that the BC-algorithm works quite successfully in spite of...

The change in electric potential due to lightning

William W. Hager, Beyza Caliskan Aslan (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

The change in the electric potential due to lightning is evaluated. The potential along the lightning channel is a constant which is the projection of the pre-flash potential along a piecewise harmonic eigenfunction which is constant along the lightning channel. The change in the potential outside the lightning channel is a harmonic function whose boundary conditions are expressed in terms of the pre-flash potential and the post-flash potential along the lightning channel. The expression for the...

The density of states of a local almost periodic operator in ℝ ν

Andrzej Krupa (2003)

Studia Mathematica

We prove the existence of the density of states of a local, self-adjoint operator determined by a coercive, almost periodic quadratic form on H m ( ℝ ν ) . The support of the density coincides with the spectrum of the operator in L ² ( ℝ ν ) .

Un problème Spectral Issu d'un Couplage Elasto-Acoustique

Mario Durán, Jean-Claude Nédélec (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We are interested in the theoretical study of a spectral problem arising in a physical situation, namely interactions of fluid-solid type structure. More precisely, we study the existence of solutions for a quadratic eigenvalue problem, which describes the vibrations of a system made up of two elastic bodies, where a slip is allowed on their interface and which surround a cavity full of an inviscid and slightly compressible fluid. The problem shall be treated like a generalized eigenvalue...

Currently displaying 61 – 80 of 89