Parabolic partial differential equations

partial differential equation for distribution of heat in a given region over time

partial differential equation

equation that describes density changes of a material that is diffusing in a medium

class of second-order linear partial differential equations

formula relating stochastic processes to partial differential equations

combination of the diffusion and convection (advection) equations

type of mathematical model

how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state

fundamental solution to the heat equation, given boundary values

1952 article by Alan Turing

Autowaves are self-supporting non-linear waves in active media (i.e. those that provide distributed energy sources). The term is generally used in processes where the waves carry relatively low energy, which is necessary for synchronization or switching the active medium.