Think of \begin{center} \( u_{tt} + 2au_t + Au = 0 \) \end{center} as a wave equation. Bounded solutions of this equation tend to solutions of the heat equation \begin{center} \( 2av_t + Av = 0. \) \end{center} This asymptotic parabolicity result is due to Furth, Ornstein and Taylor (1917-1922). In 2002 Cascaval, Eckstein, Frota and J. Goldstein [CEFG] replaced \( A = -D^2 =-\left(\frac{d}{dx}\right)^2 \) by \( A^{\alpha} \), \( 0 < \alpha < 1 \). Included were calculations which allowed the friction to be replaced by a stronger friction term. This leads to a different limiting equation \begin{center} \( 2aA^b v_t + Av = 0 \) \end{center} for \( 0 < b < \frac{1}{2} \). The stronger friction term leads to a number of complications.