19 citations · 62 across the 29 of their papers we have counts for
29 papers
The BGK model with in-flow boundary condition: forward and inverse problems
Ru-Yu Lai, Hanming Zhou
We study the Bhatnagar-Gross-Krook (BGK) equation in a bounded domain with in-flow boundary condition. The BGK model is a simple relaxation of the Boltzmann equation through replac…
Inverse problems for time-dependent nonlinear transport equations
Ru-Yu Lai, Hanming Zhou
In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds a…
Partial Data Inverse Problems for the Nonlinear Schrödinger Equation
Ru-Yu Lai, Xuezhu Lu, Ting Zhou
In this paper we prove the uniqueness and stability in determining a time-dependent nonlinear coefficient in the Schrödinger equation $(i\partial_t + Δ+ q(t, x))u + βu^2…
Recovery of coefficients in semilinear transport equations
Ru-Yu Lai, Gunther Uhlmann, Hanming Zhou
We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficie…
Single pixel X-ray transform and related inverse problems
Ru-Yu Lai, Gunther Uhlmann, Jian Zhai +1
In this paper, we analyze the nonlinear single pixel X-ray transform and study the reconstruction of from the measurement . Different from the well-known X-ray transfor…
Inverse transport and diffusion problems in photoacoustic imaging with nonlinear absorption
Ru-Yu Lai, Kui Ren, Ting Zhou
Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography (PAT), we study in this work inverse coefficient problems for a semilinear radiative t…
Inverse source problems in transport equations with external forces
Ru-Yu Lai, Hanming Zhou
This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for gene…
An Inverse Problem for Non-linear Fractional Magnetic Schrodinger Equation
Ru-Yu Lai, Ting Zhou
In this paper, we study forward problem and inverse problem for the fractional magnetic Schrodinger equation with nonlinear electric potential. We first investigate the maximum pri…
Inverse problems for the fractional Laplace equation with lower order nonlinear perturbations
Ru-Yu Lai, Laurel Ohm
We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is…
Global determination for an inverse problem from the vortex dynamics
Ru-Yu Lai, Hanming Zhou
We consider the problem of reconstructing a background potential from the dynamical behavior of vortex dipole. We prove that under suitable conditions, one can uniquely reconstruct…
Partial Data Inverse Problems for Nonlinear Magnetic Schrödinger Equations
Ru-Yu Lai, Ting Zhou
We prove that the knowledge of the Dirichlet-to-Neumann map, measured on a part of the boundary of a bounded domain in , can uniquely determine, in a nonlinea…
Reconstruction of the emission coefficient in the nonlinear radiative transfer equation
Christian Klingenberg, Ru-Yu Lai, Qin Li
In this paper, we investigate an inverse problem for the radiative transfer equation that is coupled with a heat equation in a nonscattering medium in , . Th…
Inverse problems for fractional semilinear elliptic equations
Ru-Yu Lai, Yi-Hsuan Lin
This paper is concerned with the forward and inverse problems for the fractional semilinear elliptic equation for . For the forward problem, we proved t…
Reconstruction of the collision kernel in the nonlinear Boltzmann equation
Ru-Yu Lai, Gunther Uhlmann, Yang Yang
We consider an inverse problem for the Boltzmann equation with nonlinear collision operator in dimensions . We show that the kinetic collision kernel can be uniquely deter…
On diffusive scaling in acousto-optic imaging
Francis J. Chung, Ru-Yu Lai, Qin Li
Acousto-optic imaging (AOI) is a hybrid imaging process. By perturbing the to-be-reconstructed tissues with acoustic waves, one introduces the interaction between the acoustic and…
The Calderón problem for a space-time fractional parabolic equation
Ru-Yu Lai, Yi-Hsuan Lin, Angkana Rüland
In this article we study an inverse problem for the space-time fractional parabolic operator with in any space dimension. We uniquely determine the unk…
Parameter Reconstruction for general transport equation
Ru-Yu Lai, Qin Li
We consider the inverse problem for the general transport equation with external field, source term and absorption coefficient. We show that the source and the absorption coefficie…
Boundary determination of electromagnetic and Lamé parameters with corrupted data
Pedro Caro, Ru-Yu Lai, Yi-Hsuan Lin +1
We study boundary determination for an inverse problem associated to the time-harmonic Maxwell equations and another associated to the isotropic elasticity system. We identify the…
Inverse problems for the stationary transport equation in the diffusion scaling
Ru-Yu Lai, Qin Li, Gunther Uhlmann
We consider the inverse problem of reconstructing the optical parameters of the radiative transfer equation (RTE) from boundary measurements in the diffusion limit. In the diffusiv…
Quench detection on a superconducting radio-frequency cavity
Ru-Yu Lai, Daniel Spirn
We study quench detection in superconducting accelerator cavities cooled with He-II. A rigorous mathematical formula is derived to localize the quench position from dynamical data…
Global uniqueness for the semilinear fractional Schrödinger equation
Ru-Yu Lai, Yi-Hsuan Lin
We study global uniqueness in an inverse problem for the fractional semilinear Schrödinger equation with . We show that an unknown function $q(x,u)…
Nonparaxial Near-nondiffracting Accelerating Optical Beams
Ru-Yu Lai, Ting Zhou
We show that new families of accelerating and almost nondiffracting beams (solutions) for Maxwell's equations can be constructed. These are complex geometrical optics (CGO) solutio…
An inverse problem from condense matter physics
Ru-Yu Lai, Ravi Shankar, Daniel Spirn +1
We consider the problem of reconstructing the features of a weak anisotropic background potential by the trajectories of vortex dipoles in a nonlinear Gross-Pitaevskii equation. At…
Applications of CGO Solutions on Coupled-Physics Inverse Problems
Ilker Kocyigit, Ru-Yu Lai, Lingyun Qiu +2
This paper surveys inverse problems arising in several coupled-physics imaging modalities for both medical and geophysical purposes. These include Photo-acoustic Tomography (PAT),…