17 citations · 100 across the 21 of their papers we have counts for
22 papers
Identifying unknown time delay and spatially varying coefficients in a reaction-diffusion equation from boundary measurements
Ming-Hui Ding, Hongyu Liu, Catharine W. K. Lo
This work investigates an inverse problem for a general class of linear reaction-diffusion systems incorporating multiple delayed contributions, namely retarded diffusion, retarded…
Determining habitat anomalies in cross-diffusion predator-prey chemotaxis models
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
This paper addresses an open inverse problem at the interface of mathematical analysis and spatial ecology: the unique identification of unknown spatial anomalies -- interpreted as…
Parameter Identification in Reaction-Diffusion-Chemotaxis Systems from Single Turing Pattern Amplitudes
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
Turing patterns encode key information about biological mechanisms, yet traditional inverse problems rely on non-biological data like boundary measurements, neglecting the patterns…
Determining a parabolic-elliptic-elliptic system by boundary observation of its non-negative solutions under chemotaxis background
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
This paper addresses a profoundly challenging inverse problem that has remained largely unexplored due to its mathematical complexity: the unique identification of all unknown coef…
Determining evolutionary equations from a single passive boundary observation
Lu Chen, Yan Jiang, Hongyu Liu +2
We study inverse boundary problems for evolutionary PDEs using only a single passive boundary observation, where data from an unknown internal source propagate through an unknown m…
Inverse Problems for Mean Field Games
Hongyu Liu, Catharine W. K. Lo, Shen Zhang
In this book, we present a curated collection of existing results on inverse problems for Mean Field Games (MFGs), a cutting-edge and rapidly evolving field of research. Our aim is…
Simultaneously decoding the unknown stationary state and function parameters for mean field games
Hongyu Liu, Catharine W. K. Lo
Mean field games (MFGs) offer a versatile framework for modeling large-scale interactive systems across multiple domains. This paper builds upon a previous work, by developing a st…
Inverse problems for coupled nonlocal nonlinear systems arising in mathematical biology
Ming-Hui Ding, Hongyu Liu, Catharine W. K. Lo
In this paper, we propose and study several inverse problems of determining unknown parameters in nonlocal nonlinear coupled PDE systems, including the potentials, nonlinear intera…
Determining state space anomalies in mean field games
Hongyu Liu, Catharine W. K. Lo
In this paper, we are concerned with the inverse problem of determining anomalies in the state space associated with the stationary mean field game (MFG) system. We establish novel…
On the Obstacle Problem in Fractional Generalised Orlicz Spaces
Catharine W. K. Lo, José Francisco Rodrigues
We consider the one and the two obstacles problems for the nonlocal nonlinear anisotropic -Laplacian , with . We prove the strict T-monotonicity of $\mat…
Decoding a mean field game by the Cauchy data around its unknown stationary states
Hongyu Liu, Catharine W. K. Lo, Shen Zhang
In recent years, mean field games (MFGs) have garnered considerable attention and emerged as a dynamic and actively researched field across various domains, including economics, so…
On inverse problems in multi-population aggregation models
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
This paper focuses on inverse problems arising in studying multi-population aggregations. The goal is to reconstruct the diffusion coefficient, advection coefficient, and interacti…
On the Stability of the -Nonlocal -Obstacle Problem and their Coincidence Sets and Free Boundaries
Catharine W. K. Lo, José Francisco Rodrigues
We show that the solutions to the nonlocal obstacle problems for the nonlocal operator, when the fractional parameter for , converge to the solution of t…
On inverse problems in predator-prey models
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
In this paper, we consider the inverse problem of determining the coefficients of interaction terms within some Lotka-Volterra models, with support from boundary observation of its…
Determining Sources in the Bioluminescence Tomography Problem
Ming-Hui Ding, Rongfang Gong, Hongyu Liu +1
In this paper, we revisit the bioluminescence tomography (BLT) problem, where one seeks to reconstruct bioluminescence signals (an internal light source) from external measurements…
Strong uniqueness principle for fractional polyharmonic operators and applications to inverse problems
Ching-Lung Lin, Hongyu Liu, Catharine W. K. Lo
In this work, we are concerned with inverse problems involving poly-fractional operators, where the poly-fractional operator is of the form \[P( (-Δ_g)^s)u := \sum_{i=1}^M α_i(-Δ_{…
Determining a parabolic system by boundary observation of its non-negative solutions with biological applications
Hongyu Liu, Catharine W. K. Lo
In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative soluti…
Global Existence for Nonlocal Quasilinear Diffusion Systems in Non-Isotropic Non-Divergence Form
Catharine W. K. Lo, José Francisco Rodrigues
Consider the quasilinear diffusion problem \[\begin{cases}\mathbf{u}'+Π(t,x,\mathbf{u},Σ\mathbf{u})\mathbb{A}\mathbf{u}=\mathbf{f}(t,x,\mathbf{u},Σ\mathbf{u})&\text{ in }]0,T[\time…
On an Anisotropic Fractional Stefan-Type Problem with Dirichlet Boundary Conditions
Catharine W. K. Lo, José Francisco Rodrigues
In this work, we consider the fractional Stefan-type problem in a Lipschitz bounded domain with time-dependent Dirichlet boundary condition for the temperatu…
On a Class of Nonlocal Obstacle Type Problems Related to the Distributional Riesz Fractional Derivative
Catharine W. K. Lo, José Francisco Rodrigues
In this work, we consider the nonlocal obstacle problem with a given obstacle in a bounded Lipschitz domain in , such that $\mathbb{K}_ψ^s=\{v\in H^s_0(Ω):v…
Quantum Invariants of 3-manifolds and NP vs #P
Gorjan Alagic, Catharine Lo
The computational complexity class #P captures the difficulty of counting the satisfying assignments to a boolean formula. In this work, we use basic tools from quantum computation…
F-zeta geometry, Tate motives, and the Habiro ring
Catharine Wing Kwan Lo, Matilde Marcolli
In this paper we propose different notions of F_zeta-geometry, for zeta a root of unity, generalizing notions of F_1-geometry (geometry over the "field with one element") based on…