14.  Physics applications

14.1  Reaction-diffusion systems

A reaction-diffusion system is classically described mathematically by semi-linear parabolic partial differential equations. These systems are used in physics (in the broadest sense): biology, chemistry, ecology, geology, etc., to describe the evolution of concentrations of one or more substances spatially distributed and subject to both a diffusion and a reaction process.

The most basic reaction-diffusion equation deals with a single substance and is called Fisher's reaction-diffusion equation (1937). This equation is formulated as follows in U × ]0,t _m [ where $U\subseteq ℝ$...