We investigate the behavior of the solutions of the problem
\begin{displaymath}\begin{array}{*{20}{c}} {{u_t} = {u_{xx}} - \alpha u - \upsil... ... h(t),} & {{u_x}(L,t) = {\upsilon _x}(L,t) = 0} \\ \end{array} \end{displaymath} where $ t \geqslant 0$ $ 0 < x < L \leqslant \infty $ Solutions of the above equations are considered a qualitative model of conduction of nerve axon impulses. Using explicit constructions and semigroup methods, we obtain decay results on the norms of differences between the solution for $ L$ is large but finite. We conclude that nerve impulses for long finite nerves become uniformly close to those of the semi-infinite nerves away from the right endpoint of the finite nerve.