Related papers: Inverse hyperbolic problems and optical black hole…
This paper consists of two parts. In the first part we describe the recent works on the inverse problems for the wave equation in $(n+1)$-dimensional space equipped with pseudo-Riemannian metric with Lorentz signature. We study the…
We study the inverse problems for the second order hyperbolic equations of general form with time-dependent coefficients assuming that the boundary data are given on a part of the boundary. The main result of this paper is the determination…
We describe the general setting for the optical Aharonov-Bohm effect based on the inverse problem of the identification of the coefficients of the governing hyperbolic equation by the boundary measurements. We interpret the inverse problem…
The 3+1 Hamiltonian formulation in the gauge $D_tN=-K$ on the lapse function fixes the direction of time associated with the trace $K$ of the extrinsic curvature tensor. The Hamiltonian equations hereby become hyperbolic. We study this new…
We give a survey of author's results on the inverse hyperbolic problems with time-dependent and time-independent coefficients. We consider the case of hyperbolic equations with Yang-Mills potentials and the case of domains with obstacles.…
The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…
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…
In this paper, a nonlinear inverse boundary value problem for the second-order hyperbolic equation with nonlocal conditions is studied. To investigate the solvability of the original problem, we first consider an auxiliary inverse boundary…
We demonstrate that light is subject to anomalous (i.e., negative) diffraction when propagating in the presence of hyperbolic dispersion. We show that light propagation in hyperbolic media resembles the dynamics of a quantum particle of…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
In this work we study the inverse problem related to the emission of Hawking radiation. We first show how the knowledge of greybody factors of different angular contributions $l$ can be used to constrain the width of the corresponding black…
We study the spectral theory and inverse problem on asymptotically hyperbolic manifolds. The main subjects are as follows: (1)Location of the essential spectrum. (2)Absence of eigenvalues embedded in the continuous spectrum. (3)Limiting…
There are two main approaches to solve inverse coefficient determination problems for wave equations: the Boundary Control method and an approach based on geometric optics. These notes focus on the Boundary Control method, but we will have…
We prove global Lipschitz stability for inverse source and coefficient problems for first-order linear hyperbolic equations, the coefficients of which depend on both space and time. We use a global Carleman estimate, and a crucial point,…
The paper introduces a method to solve inverse problems for hyperbolic systems where the leading order terms are non-linear. We apply the method to the coupled Einstein-scalar field equations and study the question whether the structure of…
In this article, we provide a modified argument for proving the conditional stability of inverse source problem for a hyperbolic equation. Our method does not require any extension of solution with respect to time and therefore simplifies…
Black hole solutions in the context of a generic matter-coupled two-dimensional dilaton gravity theory are discussed both at the classical and semiclassical level. Starting from general assumptions, a criterion for the existence of black…
The news function providing some relevant information about angular distribution of gravitational radiation in axisymmetric black hole collisions at the speed of light had been evaluated in the literature by perturbation methods, after…
A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.
We study the inverse problem for the second order self-adjoint hyperbolic equation with the boundary data given on a part of the boundary. This paper is the continuation of the author's paper [E]. In [E] we presented the crucial local step…