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fokker-planck_equation [2013/09/17 14:31]
nikolaj
fokker-planck_equation [2014/03/21 11:11] (current)
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 ===== Fokker-Planck equation ===== ===== Fokker-Planck equation =====
-==== Definition ​==== +==== Set ==== 
-| @#88DDEE: $ n\in\mathbb N $ | +| @#55CCEE: context ​    | @#55CCEE: $ n\in\mathbb N $ | 
-| @#88DDEE: $ \mu:​C(\mathbb R^n,\mathbb R^n) $ | +| @#55CCEE: context ​    | @#55CCEE: $ \mu:​C(\mathbb R^n,\mathbb R^n) $ | 
-| @#88DDEE: $ D:​C^2(\mathbb R^n,\mathbb R^{n^2}) $ |+| @#55CCEE: context ​    | @#55CCEE: $ \mathsf{D}:​C^2(\mathbb R^n,\mathbb R^{n^2}) $ | 
 +| @#DDDDDD: range       | @#DDDDDD: $ ::​\mu(\mathbf{x}) $ | 
 +| @#DDDDDD: range       | @#DDDDDD: $ ::​\mathsf{D}(\mathbf{x}) $ |
  
-| @#FFBB00: $ f \in \mathrm{it} $ |+| @#FFBB00: definiendum ​| @#FFBB00: $ f \in \mathrm{it} $ |
  
-| @#55EE55: $ f:​C^2(\mathbb R^n\times\mathbb R,\mathbb R) $  |+| @#55EE55: postulate ​  | @#55EE55: $ f:​C^2(\mathbb R^n\times\mathbb R,\mathbb R) $  ​
 +| @#DDDDDD: range       | @#DDDDDD: $ ::​f(\mathbf{x},​t) ​ $ |
  
-| @#DDDDDD$ ::​f(\mathbf{x},​t) ​ $ | +| @#55EE55postulate ​  | @#55EE55: $ \frac{\partial }{\partial t} f = -\mathrm{div} (\mu \cdot f) + \sum_{i=1}^{n} \sum_{j=1}^{n} \frac{\partial^2}{\partial x_i \, \partial x_j} (\mathsf{D}_{ij}\cdot f) $ |
-| @#DDDDDD: $ ::​\mu(\mathbf{x}) $ | +
-| @#DDDDDD: $ ::​\mathsf{D}(\mathbf{x}) $ | +
- +
-| @#55EE55: $ \frac{\partial }{\partial t} f = -\mathrm{div} (\mu \cdot f) + \sum_{i=1}^{n} \sum_{j=1}^{n} \frac{\partial^2}{\partial x_i \, \partial x_j} (\mathsf{D}_{ij}\cdot f) $ |+
  
 ==== Discussion ==== ==== Discussion ====
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