A weak solution approach to a reaction--diffusion system modeling pattern formation on seashells

, and . Mathematical Methods in the Applied Sciences 32 (17): 2267--2286 (2009)


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.

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