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.
On démontre dans cet article des versions probabilistes des injections de Sobolev sur une variété riemannienne compacte, . Plus précisément on démontre que pour des mesures de probabilité naturelles sur l’espace , presque toute fonction appartient à tous les espaces , . On donne ensuite des applications à l’étude des harmoniques sphériques sur la sphère : on démontre (encore pour des mesures de probabilité naturelles) que presque toute base hilbertienne de formée d’harmoniques sphériques...
Dans ce travail, nous considérons un opérateur différentiel simple ainsi que des perturbations. Alors que le spectre de l’opérateur non-perturbé est confiné à une droite à l’intérieur du pseudospectre, nous montrons pour les opérateurs perturbés que les valeurs propres se distribuent à l’intérieur du pseudospectre d’après une loi de Weyl.
In this paper the stability of two basic types of cable stayed bridges, suspended by one or two rows of cables, is studied. Two linearized models of the center span describing the vertical and torsional oscillations are investigated. After the analysis of these models, a stability criterion is formulated. The criterion expresses a relation between the eigenvalues of the vertical and torsional oscillations of the center span. The continuous dependence of the eigenvalues on some data is studied and...
We study the problem of existence of orbits connecting stationary points for the nonlinear heat and strongly damped wave equations being at resonance at infinity. The main difficulty lies in the fact that the problems may have no solutions for general nonlinearity. To address this question we introduce geometrical assumptions for the nonlinear term and use them to prove index formulas expressing the Conley index of associated semiflows. We also prove that the geometrical assumptions are generalizations...
We consider the problem of reconstructing an cell matrix constructed from a vector of positive real numbers, from a given set of spectral data. In addition, we show that the spectra of cell matrices and are the same for every permutation .