  The Kolmogrov-Johnson-Mehl-Avrami (KJMA) growth model is considered on a
one-dimensional (1D) lattice. Cells can growth with constant speed and
continuously nucleate on the empty sites. We offer an alternative, mean-field
like approach for describing theoretically the dynamics and derive an
analytical cell-size distribution function. Our method reproduces the same
scaling laws as the KJMA theory and has the advantage that it leads to a simple
closed form for the cell-size distribution function. It is shown that a Weibull
distribution is appropriate for describing the final cell-size distribution.
The results are discussed in comparison with Monte Carlo simulation data.
