We investigate a reaction--diffusion system proposed by H. Meinhardt
as a model for pattern formation on seashells. We give a new proof
for the existence of a local weak solution for general initial conditions
and parameters upon using an iterative approach. Furthermore, the
solution is shown to exist globally for suitable initial data. The
behavior of the solution in time and space is illustrated through
numerical simulations. Copyright � 2009 John Wiley & Sons, Ltd.