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LaTeX Math Block
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p(t,r) = p_i + \frac{q_t}{4 \pi \sigma} {\rm Ei} \left(-\frac{r^2}{4 \chi t} \right)



Approximations

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Middle Time Response and Late-time response

LaTeX Math Inline
body\displaystyle t \gg \frac{r^2}{4\chi}


LaTeX Math Block
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p(t,r) \sim p_i + \frac{q_t}{4 \pi \sigma} \left[  
\gamma + \ln \left(\frac{r^2}{4 \chi t} \right) \right] 

= p_i - \frac{q_t}{4 \pi \sigma} \ln \left(\frac{2.24585 \, t}{r^2} \right)


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