相关论文: On one inverse spectral problem relatively domain

When considering fractional diffusion equation as model equation in analyzing anomalous diffusion processes, some important parameters in the model related to orders of the fractional derivatives, are often unknown and difficult to be…

The algorithm for generation of exact solutions of the nonlinear equation in partial derivatives of a divergent type which is included in the formulation of magnetostatics, hydro-and aerodynamics, quantum mechanics (stationary Schr\"odinger…

An application of dimensional reduction results for gradient constrained problems is provided for 3D-2D dimension reduction for supremal functionals, in the case when the domain is convex.

We show global uniqueness in an inverse problem for the fractional Schr\"odinger equation: an unknown potential in a bounded domain is uniquely determined by exterior measurements of solutions. We also show global uniqueness in the partial…

An inverse problem is considered for an inhomogeneous Schr\"odinger equation. Assuming that the potential vanishes outside a finite interval and satisfies some other technical assumptions, one proves the uniqueness of the recovery of this…

A discrete version of the two-dimensional inverse scattering problem is considered. On this basis, algebraic transformations for the two-dimensional finite-difference Schredinger equation are elaborated.

We consider the inverse problem of the determining the potential in the dynamical Schr\"odinger equation on the interval by the measurement on the whole boundary. Provided that source is \emph{generic} using the Boundary Control method we…

In this work, we study the inverse spectral problem, using the Weyl matrix as the input data, for the matrix Schrodinger operator on the half-line with the boundary condition being the form of the most general self-adjoint. We prove the…

We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship…

We present a definition of the two-sided inverse of position operator in general case of deformed Heisenberg algebra leading to minimal length. Energy spectrum and eigenfunctions in momentum space for 1D Coulomb-like potential in deformed…

This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…

Concerning the Laplace operator with homogeneous Dirichlet boundary conditions, the classical notion of isospectrality assumes that two domains are related when they give rise to the same spectrum. In two dimensions, non isometric,…

In this article, we present explicit estimates of the size of the domain on which the Implicit Function Theorem and the Inverse Function Theorem are valid. For maps that are twice continuously differentiable, these estimates depend upon the…

The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…

The stated paper is dedicated to one of the inverse problems of spectral theory. It is necessary to define matrix (constant) coefficients of some quadratic pencil, if the eigenvalues of this pencil are known. Furthermore, it is known that…

Non-self-adjoint second-order ordinary differential operators on a finite interval with complex weights are studied. Properties of spectral characteristics are established and the inverse problem of recovering operators from their spectral…

The random forced Navier-Stokes equation can be obtained as a variational problem of a proper action. In virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large…

We study the optimal domain for the Hardy operator considered with values in a rearrangement invariant space. In particular, this domain can be represented as the space of integrable functions with respect to a vector measure defined on a…

The inverse scattering problem for the Schr$\mathrm{\ddot{o}}$dinger operators on the line is considered when the potential is real valued and integrable and has a finite first moment. It is shown that the potential on the line is uniquely…

In this paper the first and second domain variation for functionals related to elliptic boundary and eigenvalue problems with Robin boundary conditions is computed. Minimality and maximality properties of the ball among nearly circular…