Partial differential equations (PDEs) are mathematical equations that involve multiple independent variables and their partial derivatives. They are used to model a wide range of physical phenomena in fields such as physics, engineering, biology, and finance. Research in the area of partial differential equations aims to study the properties of these equations, develop methods for solving them analytically and numerically, and investigate their applications in various scientific disciplines. Some key topics of research in PDEs include existence and uniqueness of solutions, classification of different types of PDEs, well-posedness of initial and boundary value problems, stability of solutions, and the development of numerical methods for solving PDEs. Overall, research in partial differential equations plays a crucial role in advancing our understanding of complex systems and in developing tools for solving real-world problems.