  The Luria-Delbr\"uck mutation model has a long history and has been
mathematically formulated in several different ways. Here we tackle the problem
in the case of a continuous distribution using some mathematical tools from
nonlinear statistical physics. Starting from the classical formulations we
derive the corresponding differential models and show that under a suitable
mean field scaling they correspond to generalized Fokker-Planck equations for
the mutants distribution whose solutions are given by the corresponding
Luria-Delbr\"uck distribution. Numerical results confirming the theoretical
analysis are also presented.
