Diffusion Equations
Diffusion Equations
The famous diffusion equation, also known as the heat equation, reads $$\frac{\partial u}{\partial t}=\alpha\frac{\partial^{2}u}{\partial x^{2}},$$ where $$u(x,t)$$ is the unknown function to be solved for, x is a coordinate in space, and t is time. The coefficient α is the diffusion coefficient and determines how fast u changes in time. …