Related papers: Solution of the inverse spectral problem for a con…
In this study, the theorem on necessary and sufficient conditions for the solvability of inverse problem for Sturm-Liouville operator with discontinuous coefficient is proved and the algorithm of reconstruction of potential from spectral…
Recently, there appeared a significant interest in inverse spectral problems for non-local operators arising in numerous applications. In the present work, we consider the operator with frozen argument $ly = -y''(x) + p(x)y(x) + q(x)y(a),$…
We study inverse spectral problems for ordinary differential equations with regular singularities on compact star-type graphs when differential equations have different orders on diferent edges. As the main spectral characteristics we…
Applying the inverse scattering transform to study a focusing two-component Hirota equation with nonzero boundary conditions at infinity. Through the spectral problem and the adjoint spectral problem, the analyticity properties and symmetry…
This paper addresses the inverse problem of simultaneously recovering multiple unknown parameters for semilinear wave equations from boundary measurements. We consider an initial-boundary value problem for a wave equation with a general…
Given a quantum semitoric system composed of pseudodifferential operators, Berezin-Toeplitz operators, or a combination of both, we obtain explicit formulas for recovering, from the semiclassical asymptotics of the joint spectrum, all…
In this paper, the Sturm-Liouville problem with nonseparated quasiperiodic boundary conditions is considered. We study the recovery of the problem parameters from the Hill-type discriminant, the Dirichlet spectrum, and the sequence of…
For a given self-adjoint operator $A$ with discrete spectrum, we completely characterize possible eigenvalues of its rank-one perturbations~$B$ and discuss the inverse problem of reconstructing $B$ from its spectrum.
We study an inverse scattering problem of a perturbed biharmonic operator. we show that the high-frequency asymptotic of scattering amplitude of the biharmonic operator uniquely determine the curl A and {V -1/2 nablaA}. We also study the…
Spectral problem for a self-adjoint third-order differential operator with non-local potential on a finite interval is studied. Elementary functions that are analogues of sines and cosines for such operators are described. Direct and…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we…
We give a short review of results on inverse spectral problems for ordinary differential operators on a spatial networks (geometrical graphs). We pay the main attention to the most important nonlinear inverse problems of recovering…
We consider second order linear differential operators possessing a term depending on the unknown function with a fixed argument and study the uniqueness of recovering the operators from the spectrum. We also obtain a constructive procedure…
This paper deals with an inverse nodal problem for the Dirac differential operator with the discontinuity conditions inside the interval. We obtain a new approach for asymptotic expressions of the solutions and prove that the coefficients…
We consider inverse eigenvalue problems for the perturbed Bessel operator in $L^{2}(0,1)$. (1) For the case where the angular-momentum quantum number $\ell\in\mathbb{N}\cup\{0\}$, we establish a uniqueness result for the inverse spectral…
The spectral properties of Dirac operators on $(0,1)$ with potentials that belong entrywise to $L_p(0,1)$, for some $p\in[1,\infty)$, are studied. The algorithm of reconstruction of the potential from two spectra or from one spectrum and…
We study inverse boundary problems for a one dimensional linear integro-differential equation of the Gurtin--Pipkin type with the Dirichlet-to-Neumann map as the inverse data. Under natural conditions on the kernel of the integral operator,…
This article is concerned with an inverse problem of simultaneously determining a spatially varying coefficient and a Robin coefficient for a one-dimensional fractional diffusion equation with a time-fractional derivative of order…
The inverse Robin problem covers the determination of the Robin parameter in an elliptic partial differential equation posed on a domain $\Omega$. Given the solution of the Robin problem on a subdomain $\omega \subset \Omega$ together with…