Inverse problem for a nonlinear Helmholtz equation
Inverse problem for a physiologically structured population model with variable-effort harvesting
We consider the inverse problem of determining how the physiological structure of a harvested population evolves in time, and of finding the time-dependent effort to be expended in harvesting, so that the weighted integral of the density, which may be, for example, the total number of individuals or the total biomass, has prescribed dynamics. We give conditions for the existence of a unique, global, weak solution to the problem. Our investigation is carried out using the method of characteristics...
Inverse Problem for Fractional Diffusion Equation
MSC 2010: 26A33, 33E12, 34K29, 34L15, 35K57, 35R30We prove that by taking suitable initial distributions only finitely many measurements on the boundary are required to recover uniquely the diffusion coefficient of a one dimensional fractional diffusion equation. If a lower bound on the diffusion coefficient is known a priori then even only two measurements are sufficient. The technique is based on possibility of extracting the full boundary spectral data from special lateral measurements.
Inverse problem for semilinear ultraparabolic equation of higher order
We study the existence and the uniqueness of the weak solution of an inverse problem for a semilinear higher order ultraparabolic equation with Lipschitz nonlinearity. The main aim is to determine the weak solution of the equation and some functions that depend on the time variable, appearing on the right-hand side of the equation. The overdetermination conditions introduced are of integral type. In order to prove the solvability of this problem in Sobolev spaces we use the Galerkin method and the...
Inverse problems and microlocal analysis
Inverse problems for memory kernels by Laplace transform methods.
Inverse problems for periodic transport equations
Inverse Scattering at fixed energy for stratified media
Inverse scattering for the one-dimensional Stark effect and application to the cylindrical KdV equation
Inverse Scattering for Waveguides
We study the inverse scattering problem for a waveguide with cylindrical ends, , where each has a product type metric. We prove, that the physical scattering matrix, measured on just one of these ends, determines up to an isometry.
Inverse scattering problem for moving obstacles.
Inverse scattering problems in several dimensions
Inverse scattering theory for Dirac operators
Inverse scattering via nonlinear integral equations method for a sound-soft crack with phaseless data
We consider the inverse scattering of time-harmonic plane waves to reconstruct the shape of a sound-soft crack from a knowledge of the given incident field and the phaseless data, and we check the invariance of far field data with respect to translation of the crack. We present a numerical method that is based on a system of nonlinear and ill-posed integral equations, and our scheme is easy and simple to implement. The numerical implementation is described and numerical examples are presented to...
Inverse source problem in a 3D ball from best meromorphic approximation on 2D slices.
Inverse spectral problem for the Schrödinger operator with periodic magnetic and electric potentials
Invisible obstacles
It is proved that one can choose a control function on an arbitrarilly small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number will be as small as one wishes. The obstacle is called "invisible" in this case.