相关论文: The Identification Problem for the attenuated X-ra…
The first part of this paper is concerned with the uniqueness to inverse time-harmonic elastic scattering from bounded rigid obstacles in two dimensions. It is proved that a connected polygonal obstacle can be uniquely identified by the…
We consider a scalar conservation law with a spatially discontinuous flux at a single point $x=0$, and we study the initial data identification problem for $AB$-entropy solutions associated to an interface connection $(A,B)$. This problem…
The Schroedinger equation is considered on the line when the potential is real valued, compactly supported, and square integrable. The nonuniqueness is analyzed in the recovery of such a potential from the data consisting of the ratio of a…
This work is devoted to the analysis of the backward problem for a viscous Hamilton-Jacobi equation with degenerate diffusion and a general Hamiltonian that is not necessarily quadratic. First, we focus on linear degenerate parabolic…
For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…
We consider the formally determined inverse problem of recovering an unknown time-dependent potential function from the knowledge of the restriction of the solution of the wave equation to a small subset, subject to a single external…
We study the cohomological equation $Xu=f$ for smooth locally Hamiltonian flows on compact surfaces. The main novelty of the proposed approach is that it is used to study the regularity of the solution $u$ when the flow has saddle loops,…
Hamiltonian Learning is a process of recovering system Hamiltonian from measurements, which is a fundamental problem in quantum information processing. In this study, we investigate the problem of learning the symmetric Hamiltonian from its…
First, we review existing attenuation models and discuss their causality properties, which we believe to be essential for algorithms for inversion with attenuated data. Then, we survey causality properties of common attenuation models. We…
The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time scales and is often referred to as {\it the\/} diffusion…
Hamiltonian Learning (HL) is essential for validating quantum systems in quantum computing. Not all Hamiltonians can be uniquely recovered from a steady state. HL success depends on the Hamiltonian model and steady state. Here, we analyze…
We are concerned with the inverse boundary problem of determining anomalies associated with a semilinear elliptic equation of the form $-\Delta u+a(\mathbf x, u)=0$, where $a(\mathbf x, u)$ is a general nonlinear term that belongs to a…
We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the…
This paper has been withdrawn. Consider an isolated complex hypersurface singularity, f(x_1,..,x_n)=0. For Newton-non-degenerate singularities the local topology is completely determined by an associated polyhedral object, the Newton…
We consider the Hamiltonian renormalisation group flow of discretised one-dimensional physical theories. In particular, we investigate the influence the choice of different embedding maps has on the RG flow and the resulting continuum…
We consider the problem of recovering a signal from nonlinear transformations, under convex constraints modeling a priori information. Standard feasibility and optimization methods are ill-suited to tackle this problem due to the…
In this paper, we study small data solutions to the Vlasov-Poisson system with the simplest external potential, for which unstable trapping holds for the associated Hamiltonian flow. First, we provide a new proof of global existence for…
The paper considers recovery of signals from incomplete observations and a problem of determination of the allowed quantity of missed observations, i.e. the problem of determination of the size of the uniqueness sets for a given data…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
We prove the existence and uniqueness of strong solutions to the equation $u u_x - u_{yy} = f$ in the vicinity of the linear shear flow, subject to perturbations of the source term and lateral boundary conditions. Since the solutions we…