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...
Inequalities for the transformation operators and applications.
Initial boundary value problem for the mKdV equation on a finite interval
We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex -plane. This RH problem is determined by certain spectral functions which are defined in terms of the initial-boundary values at and . We show that the spectral functions satisfy an algebraic “global relation” which express the implicit relation between all boundary values in terms of spectral...
Invariant transformations for the Sturm--Liouville operator.
Inverse nodal problems for the Sturm-Liouville differential operators on a star-type graph.
Inverse problems connected with periods of oscillations described by ẍ + g(x) = 0
Inverse problems in the theory of analytic planar vector fields.
In this communication we state and analyze the new inverse problems in the theory of differential equations related to the construction of an analytic planar verctor field from a given, finite number of solutions, trajectories or partial integrals.Likewise, we study the problem of determining a stationary complex analytic vector field Γ from a given, finite subset of terms in the formal power series (...).
Inverse problems on star-type graphs: differential operators of different orders on different edges
We study inverse spectral problems for ordinary differential equations on compact star-type graphs when differential equations have different orders on different edges. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.
Inverse spectral analysis for singular differential operators with matrix coefficients.
Inverse spectral problems for nonlinear Sturm-Liouville problems.
Irregular Sampling and the Inverse Spectral Problem.
Isospectral Sets for AKNS Systems on the Unit Interval with Generalized Periodic Boundary Conditions.