Partial Differential Equations and Modelling

Partial Differential Equations (PDEs) are equations where the unknown is a function—or sometimes a vector field—depending on several variables, often time and space. These equations involve one or more partial derivatives of the unknown.

PDEs are ubiquitous in mathematically oriented scientific fields, including biology, physics, and engineering. On the theoretical side, key questions concern the existence, uniqueness, regularity, and stability of solutions. From a more applied perspective, an important challenge is to efficiently approximate solutions using numerical methods and computer simulations.