A new approach to inverse spectral theory. I: Fundamental formalism.
A new approach to inverse spectral theory. II: General real potentials and the connection to the spectral measure.
About one inverse problem in the theory of linear differential equations with measures as coefficients
Ambarzumian's theorem for trees.
An inverse problem for a second-order differential equation in a Banach space.
An inverse problem for Sturm-Liouville operators on the half-line having Bessel-type singularity in an interior point
We study the inverse problem of recovering Sturm-Liouville operators on the half-line with a Bessel-type singularity inside the interval from the given Weyl function. The corresponding uniqueness theorem is proved, a constructive procedure for the solution of the inverse problem is provided, also necessary and sufficient conditions for the solvability of the inverse problem are obtained.
Bäcklund-Darboux transformation for non-isospectral canonical system and Riemann-Hilbert problem.
Boundary Data Maps for Schrödinger Operators on a Compact Interval
We provide a systematic study of boundary data maps, that is, 2 × 2 matrix-valued Dirichlet-to-Neumann and more generally, Robin-to-Robin maps, associated with one-dimensional Schrödinger operators on a compact interval [0, R] with separated boundary conditions at 0 and R. Most of our results are formulated in the non-self-adjoint context. Our principal results include explicit representations of these boundary data maps in terms of the resolvent...
Cubic and quartic planar differential systems with exact algebraic limit cycles.
Determination of the diffusion operator on an interval
The inverse problem of spectral analysis for the diffusion operator with quasiperiodic boundary conditions is considered. A uniqueness theorem is proved, a solution algorithm is presented, and sufficient conditions for the solvability of the inverse problem are obtained.
Differential equations on the plane with given solutions.
The aim of this paper is to construct the analytic vector fields with given as trajectories or solutions. In particular we construct the polynomial vector field from given conics (ellipses, hyperbola, parabola, straight lines) and determine the differential equations from a finite number of solutions.
Error controlled regularization by projection.
Exact solutions of the semi-infinite Toda lattice with applications to the inverse spectral problem.
Gaps and bands of one dimensional periodic Schrödinger operators, II.
Gaps of one dimensional periodic AKNS systems.
Hybrid Taguchi-differential evolution algorithm for parameter estimation of differential equation models with application to HIV dynamics.
Identification de paramètres dans les problèmes non linéaires à données incomplètes
Identification of a Duffing oscillator under different types of excitation.
Identification of a wave equation generated by a string
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 problems for degenerate parabolic equations
This paper deals with multivalued identification problems for parabolic equations. The problem consists of recovering a source term from the knowledge of an additional observation of the solution by exploiting some accessible measurements. Semigroup approach and perturbation theory for linear operators are used to treat the solvability in the strong sense of the problem. As an important application we derive the corresponding existence, uniqueness, and continuous dependence results for different...