6 citations · 10 across the 11 of their papers we have counts for
11 papers
Recovering All Coefficients in the Schrödinger Equation With Finite Sets of Boundary Measurements
Shitao Liu, Antonio Pierrottet
We consider an inverse problem of recovering all spatial dependent coefficients in the time dependent Schrödinger equation defined on an open bounded domain in , $n\g…
Radial Basis Operator Networks
Jason Kurz, Sean Oughton, Shitao Liu
Operator networks are designed to approximate nonlinear operators, which provide mappings between infinite-dimensional spaces such as function spaces. These networks are playing an…
An Inverse Hyperbolic Problem with Application to Joint Photoacoustic Parameter Determination
Shitao Liu, Gunther Uhlmann, Yang Yang
We consider an inverse problem of recovering a parameter appearing in all levels in a second-order hyperbolic equation from a single boundary measurement. The model is motivated fr…
Recover all Coefficients in Second-Order Hyperbolic Equations from Finite Sets of Boundary Measurements
Shitao Liu, Antonio Pierrottet, Scott Scruggs
We consider the inverse hyperbolic problem of recovering all spatial dependent coefficients, which are the wave speed, the damping coefficient, potential coefficient and gradient c…
Source Reconstruction and Stability via Boundary Control of Abstract Viscoelastic Systems
Walton Green, Shitao Liu
We study the inverse source problem for a class of viscoelastic systems from a single boundary measurement in a general spatial dimension. We give specific reconstruction formula a…
A Harmonic Analysis Proof of the Boundary Observability Inequality for the Wave Equation and Visco-Elastic Equation
Walton Green, Shitao Liu, Mishko Mitkovski
In this paper, we give a harmonic analysis proof of the Neumann boundary observability inequality for the wave equation in an arbitrary space dimension. Our proof is elementary in…
An inverse boundary value problem for the magnetic Schrödinger operator with a bounded magnetic potential in a slab
Shitao Liu, Yang Yang
We study an inverse boundary value problem with partial data in an infinite slab in , , for the magnetic Schrödinger operator with an magnetic…
A Lipschitz stable reconstruction formula for the inverse problem for the wave equation
Shitao Liu, Lauri Oksanen
We consider the problem to reconstruct a wave speed in a domain from acoustic boundary measurements modelled by the hyperbolic Dirichlet-to-Neu…
Characterizations of dominated splitting system and its relation to hyperbolicity
Chun Fang, Mats Gyllenberg, Shitao Liu
Hyperbolicity and dominated splitting are two of the most important concepts in the global analysis of differentiable dynamics. In this paper we give several equivalent characteriz…
Global Uniqueness and Stability in Determining the Damping Coefficient of an Inverse Hyperbolic Problem with Non-Homogeneous Neumann B.C. through an Additional Dirichlet Boundary Trace
Shitao Liu, Roberto Triggiani
We consider a second-order hyperbolic equation on an open bounded domain in for , with -boundary $Γ=\paΩ=\bar{Γ_0\cupΓ_1}$, ,…
Inverse Problem for a Structural Acoustic Interaction
Shitao Liu
In this work, we consider an inverse problem of determining a source term for a structural acoustic partial differentia equation (PDE) model, comprised of a two or three-dimensiona…