Reaction-diffusion equations and hydrodynamic limit of interacting particle systems

Consider a physical system comprising a substantial quantity of particles that dynamically interact with each other over time. Since the number of particles is large, an explicit description of the microscopic behavior of the system becomes effectively impossible. An approach to understanding how these systems behave is to look at certain observables on a macroscopic scale, such as pressure, temperature, etc., and then to derive partial differential equations known as hydrodynamic equations which describe the evolution of the particles. In this project, we study the theoretical mechanism by which the microscopic dynamics give rise to the macroscopic ones. In particular, we are interested in systems whose hydrodynamic limit corresponds with an important class of equations known as reaction-diffusion equations. We expect to identify particle systems with the aforementioned property, and then rigorously establish the convergence to its corresponding hydrodynamic limit.

Faculty Supervisor:

Louigi Addario-Berry

Student:

Partner:

Instituto Nacional de Matematicas Pura E Aplicada

Discipline:

Mathematics

Sector:

Other

University:

McGill University

Program: