【かくさんほうていしき (diffusion equation)】
∂ f ( x , t ) ∂ t = α ( x , t ) f ( x , t ) + ∂ ∂ x [ β ( x , t ) f ( x , t ) ] + ∂ 2 ∂ x 2 [ γ ( x , t ) f ( x , t ) ] {\displaystyle {\begin{array}{l}\displaystyle {{\frac {\partial f(x,t)}{\partial t}}=\alpha (x,t)\,f(x,t)}\\\ \ \ \displaystyle {+{\frac {\partial }{\partial x}}[\beta (x,t)\,f(x,t)]+{\frac {\partial ^{2}}{\partial x^{2}}}[\gamma (x,t)\,f(x,t)]}\end{array}}\,}
の形で与えられる偏微分方程式.
![{\displaystyle {\begin{array}{l}\displaystyle {{\frac {\partial f(x,t)}{\partial t}}=\alpha (x,t)\,f(x,t)}\\\ \ \ \displaystyle {+{\frac {\partial }{\partial x}}[\beta (x,t)\,f(x,t)]+{\frac {\partial ^{2}}{\partial x^{2}}}[\gamma (x,t)\,f(x,t)]}\end{array}}\,}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/11effd7c94b2a4654251a511de1170febd68820b)