6 papers
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…
Topological Braiding and Dynamic Probing of Phase Transitions at Temporal Interfaces in Non-Hermitian Synthetic Dimensions
Yuanhang Jiang, Jianfei Li, Chengxi Yang +6
Non-Hermitian systems give rise to distinct topological phenomena, yet their manifestations at temporal interfaces characterized by abrupt changes in system parameters remain large…
Unveiling Biological Models Through Turing Patterns
Yuhan Li, Hongyu Liu, Catharine W. K. Lo
Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse prob…
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…
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…