Inverse dynamic and spectral problems for the one-dimensional Dirac system on a finite tree

We consider inverse dynamic and spectral problems for the one-dimensional Dirac system on a finite tree. Our aim will be to recover the topology of a tree (lengths and connectivity of edges) as well as the matrix potentials on each edge. As inverse data we use the Weyl–Titchmarsh matrix function or the dynamic response operator.

The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator

A final and maybe the simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a

Hyperbolic inverse boundary-value problem and time-continuation of the non-stationary Dirichlet-to-Neumann map

Let M be a compact Riemannian manifold with non-empty boundary M. In this paper we consider an inverse problem for the second-order hyperbolic initial-boundary-value problem utt + but + a(x, D)u = 0 in M R+, u|MR+ = f, u|t=0 = ut|t=0 = 0. Our goal is to determine (M, g), b and a(x, D) from the knowledge of the non-stationary Dirichlet-to-Neumann map (the hyperbolic response operator) RT, with sufficiently large T 0. The response operator RT is the map , where is the normal derivative of the solution of the initial-boundary-value problem.More specifically, we show the following. (i)It is possible to determine Rt for any t 0 if we know RT for sufficiently large T and some geometric condition upon the geodesic behaviour on (M, g) is satisfied.(ii)It is then possible to determine (M, g) and b uniquely and the elliptic operator a(x, D) modulo generalized gauge transformations.

Generalized Transient Leveque Problem

Response of an electrodiffusion friction sensor to a finite step of the wall shear rate is studied by numerically solving the relevant mass-transfer problem. The resulting numerical data on transient currents are treated further to provide reasonably accurate analytical representations. Existing approximations to the general response operator are checked by using the obtained exact solution.