The BC-method in multidimensional spectral inverse problem : theory and numerical illustrations
The BC-method in Multidimensional Spectral Inverse Problem: Theory and Numerical Illustrations
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
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
We prove the existence of the density of states of a local, self-adjoint operator determined by a coercive, almost periodic quadratic form on . The support of the density coincides with the spectrum of the operator in .
The generalized Morawetz problem for Lavrent'ev-Bitsadze equation with spectral parameter.