Concept

Reaction–diffusion system

Summary
Reaction–diffusion systems are mathematical models which correspond to several physical phenomena. The most common is the change in space and time of the concentration of one or more chemical substances: local chemical reactions in which the substances are transformed into each other, and diffusion which causes the substances to spread out over a surface in space. Reaction–diffusion systems are naturally applied in chemistry. However, the system can also describe dynamical processes of non-chemical nature. Examples are found in biology, geology and physics (neutron diffusion theory) and ecology. Mathematically, reaction–diffusion systems take the form of semi-linear parabolic partial differential equations. They can be represented in the general form :\partial_t \boldsymbol{q} = \underline{\underline{\boldsymbol{D}}} ,\nabla^2 \boldsymbol{q} + \boldsymbol{R}(\boldsymbol{q}), where q(x, t) represents the unknown vector function, is a diagonal matrix of diffusion coef
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