General information
From quantum mechanics to acoustics, chemistry to biology, and financial models to machine learning, partial differential equations (PDEs) are essential for describing the state and dynamics of systems in various environments. However, when there is a sharp change in the environment's properties—such as moving between different media or encountering abrupt shifts in dynamics—we face PDEs with singularities. While most mathematical theories for PDEs address cases with smooth or continuous changes in environmental characteristics, singular PDEs remain poorly understood. Recently, the principal investigator of this project and collaborators proposed a novel approach that promises to effectively tackle singular PDEs. This project aims to develop that approach into a general framework for singular PDEs. Additionally, it seeks to nurture young, talented Armenian mathematicians, helping them become world-class experts in this highdemand field.
