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\begin{align*}
 s(\lambda) =& (1 - \lambda) / (1 - \lambda_f), \qquad B = -2D e^{-2 \alpha r_0} (e^{\alpha r_0} - 1) / 3 \\
  E =& D_0 \left[ e^{- 2 \alpha (r - r_0)} - 2 e^{- \alpha (r - r_0)} \right] +  s(\lambda) B e^{-3\alpha(r-r_0)}, \qquad \hspace{2.85em}\lambda \geq \lambda_f,\quad r < r_c \\
  E =& \left( D_0 \left[ e^{- 2 \alpha (r - r_0)} - 2 e^{- \alpha (r - r_0)} \right] + B e^{-3\alpha(r-r_0)} \right)(\lambda/\lambda_f)^n, \qquad \lambda < \lambda_f,\quad r < r_c
\end{align*}

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