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The diffusion equation is a partial differential equation which describes density dynamics in a material undergoing diffusion. It is also used to describe processes exhibiting diffusive-like behaviour, for instance the 'diffusion' of alleles in a population in population genetics. ==Statement== The equation is usually written as: where ''ϕ''(r, ''t'') is the density of the diffusing material at location r and time ''t'' and ''D''(''ϕ'', r) is the collective diffusion coefficient for density ''ϕ'' at location r; and ∇ represents the vector differential operator del. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear. More generally, when ''D'' is a symmetric positive definite matrix, the equation describes anisotropic diffusion, which is written (for three dimensional diffusion) as: If ''D'' is constant, then the equation reduces to the following linear differential equation: : also called the heat equation. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「diffusion equation」の詳細全文を読む スポンサード リンク
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