Integro-partial differential equation

Summary

An integro-partial differential equation is an equation for an unknown function of several variables. It involves both partial derivatives of the function and integrals of it. It combines a partial differential equation with integral terms, which typically describe nonlocal interactions in space or memory in time. Main examples are the Boltzmann equation of gas dynamics, the radiative transfer equation, population balance equations and nonlocal diffusion equations. Their analysis mixes PDE methods with the theory of integral operators.