Partial differential equations are one of the most important mathematical languages to describe the world. They are not only used to describe the natural world, but also important tools to study the social behavior. Partial differential equations are ubiquitous. They appear in geometry, physics, chemistry, biology, modeling for stock market and epidemic, etc.
Mathematicians in the field of partial differential equations explain the world by studying the well-posedness theory for partial differential equations and qualitative behavior of their solutions. The partial differential equations group at Shanghai Jiao Tong University focuses on hyperbolic partial differential equations, kinetic theory and related models, regularity theory and qualitative behavior for elliptic equations, geometric partial differential equations, etc.