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LaTeX Math Block
anchorProxyBLSolution
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x_D(s) = \begin{cases}\dot f(s) \cdot t, & \mbox{if } s < s^*\\1- \dot f(s) \cdot t, & \mbox{if } s \geq s^*\end{cases}

where

LaTeX Math Inline
body--uriencoded--s%5e*

critical saturation at 

LaTeX Math Inline
body\ddot f = 0

LaTeX Math Inline
body--uriencoded--\displaystyle \dot f(s) = \frac%7Bd f%7D%7Bds%7D

first derivative of the fractional flow function

LaTeX Math Inline
body--uriencoded--\displaystyle \ddot f(s) = \frac%7Bd%5e2 f%7D%7Bds%5e2%7D

second derivative of the fractional flow function

Algebraic equation 

LaTeX Math Block Reference
anchorProxyBLSolution
can be used and used as algebraic equation to find a solution of 
LaTeX Math Block Reference
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 in terms of saturation over time and distance: 
LaTeX Math Inline
bodys(t,x)
.

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