52 citations · 371 across the 64 of their papers we have counts for
23 papers · 1 filter
Hölder Stability Estimate for a Retrospective Problem of Mean Field Games With a Non-Quadratic Hamiltonian
Michael V. Klibanov, Mikhail Y. Kokurin, Jingzhi Li
Hölder stability estimate and uniqueness are proven for a retrospective problem of Mean Field Games with a non-quadratic Hamiltonian. The previous result was only for the quadratic…
An Inverse Problem With the Final Overdetermination for the Mean Field Games System
Michael V. Klibanov, Jingzhi Li, Hongyu Liu
The mean field games (MFG) theory has broad application in mathematical modeling of social phenomena. The Mean Field Games System (MFGS) is the key to the MFG theory. This is a sys…
Hölder Stability and Uniqueness for The Mean Field Games System via Carleman Estimates
Michael V. Klibanov, Jingzhi Li, Hongyu Liu
We are concerned with the mathematical study of the Mean Field Games system (MFGS). In the conventional setup, the MFGS is a system of two coupled nonlinear parabolic PDEs of the s…
On The Mean Field Games System With the Lateral Cauchy Data via Carleman Estimates
Michael V. Klibanov, Jingzhi Li, Hongyu Liu
The second order Mean Field Games system (MFGS) in a bounded domain with the lateral Cauchy data is considered. This means that both Dirichlet and Neumann boundary data for the sol…
Boundary homogenization of a class of obstacle problems
Jingzhi Li, Hongyu Liu, Lan Tang +1
We study homogenization of a boundary obstacle problem on domain for some elliptic equations with uniformly elliptic coefficient matrices . For any $ ε\in\mathbb…
Inverse source problems in an inhomogeneous medium with a single far-field pattern
Guanghui Hu, Jingzhi Li
This paper concerns time-harmonic inverse source problems with a single far-field pattern in two dimensions, where the source term is compactly supported in an a priori given inhom…
Determining a random Schrödinger operator: both potential and source are random
Jingzhi Li, Hongyu Liu, Shiqi Ma
We study an inverse scattering problem associated with a Schrödinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scat…
Uniqueness in inverse cavity scattering problems with phaseless near-field data
Deyue Zhang, Yinglin Wang, Yukun Guo +1
This paper is concerned with the uniqueness of inverse acoustic scattering problem for cavities with the modulus of the near-fields. With the aid of the reference ball technique an…
Determining a random Schrödinger equation with unknown source and potential
Jingzhi Li, Hongyu Liu, Shiqi Ma
We are concerned with the direct and inverse scattering problems associated with a time-harmonic random Schrödinger equation with unknown source and potential terms. The well-posed…
Retrieval of acoustic sources from multi-frequency phaseless data
Deyue Zhang, Yukun Guo, Jingzhi Li +1
This paper is concerned with the inverse source problem of reconstructing an unknown acoustic excitation from phaseless measurements of the radiated fields away at multiple frequen…
Locating multiple multipolar acoustic sources using the direct sampling method
Deyue Zhang, Yukun Guo, Jingzhi Li +1
This work is concerned with the inverse source problem of locating multiple multipolar sources from boundary measurements for the Helmholtz equation. We develop simple and effectiv…
On an inverse elastic wave imaging scheme for nearly incompressible materials
Li Jingzhi, Liu Hongyu, Sun Hongpeng
This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known di…
On a gesture-computing technique using electromagnetic waves
Jingzhi Li, Hongyu Liu, Hongpeng Sun
This paper is concerned with a conceptual gesture-based instruction/input technique using electromagnetic wave detection. The gestures are modelled as the shapes of some impenetrab…
Reconstruction via the intrinsic geometric structures of interior transmission eigenfunctions
Jingzhi Li, Xiaofei Li, Hongyu Liu
We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-…
Recovering an electromagnetic obstacle by a few phaseless backscattering measurements
Jingzhi Li, Hongyu Liu, Yuliang Wang
We consider the electromagnetic scattering from a convex polyhedral PEC or PMC obstacle due to a time-harmonic incident plane wave. It is shown that the modulus of the far-field pa…
On quasi-static cloaking due to anomalous localized resonance in
Hongjie Li, Jingzhi Li, Hongyu Liu
This work concerns the cloaking due to anomalous localized resonance (CALR) in the quasi-static regime. We extend the related two-dimensional studies in [2,10] to the three-dimensi…
Recovering a polyhedral obstacle by a few backscattering measurements
Jingzhi Li, Hongyu Liu
We propose an inverse scattering scheme of recovering a polyhedral obstacle in , , by only a few high-frequency acoustic backscattering measurements. The obsta…
Inverse Elastic Scattering for Multiscale Rigid Bodies with A Single Far-field Pattern
Guanghui Hu, Jingzhi Li, Hongyu Liu +1
We develop three inverse elastic scattering schemes for locating multiple small, extended and multiscale rigid bodies, respectively. There are some salient and promising features o…
Uniqueness in Determining Refractive Indices by Formally-determined Far-field Data
Guanghui Hu, Hongyu Liu
We present two uniqueness results for the inverse problem of determining an index of refraction by the corresponding acoustic far-field measurement encoded into the scattering ampl…
Regularized Transformation-Optics Cloaking for the Helmholtz Equation: From Partial Cloak to Full Cloak
Jingzhi Li, Hongyu Liu, Luca Rondi +1
We develop a very general theory on the regularized approximate invisibility cloaking for the wave scattering governed by the Helmholtz equation in any space dimensions via the app…
Two Single-shot Methods for Locating Multiple Electromagnetic Scatterers
Jingzhi Li, Hongyu Liu, Zaijiu Shang +1
We develop two inverse scattering schemes for locating multiple electromagnetic (EM) scatterers by the electric far-field measurement corresponding to a single incident/detecting p…
Enhanced Approximate Cloaking by SH and FSH Lining
Jingzhi Li, Hongyu Liu, Hongpeng Sun
We consider approximate cloaking from a regularization viewpoint introduced in [13] for EIT and further investigated in [12] [17] for the Helmholtz equation. The cloaking schemes i…
Approximate Acoustic Cloaking in Inhomogeneous Isotropic Space
Hongyu Liu
In this paper, we consider the approximate acoustic cloaking in inhomogeneous isotropic background space. By employing transformation media, together with the use of a sound-soft l…