A weak solution approach to a reaction-diffusion system modeling pattern formation on seashells. (English) Zbl 1180.35279

Summary: 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.


35K51 Initial-boundary value problems for second-order parabolic systems
35K57 Reaction-diffusion equations
35B36 Pattern formations in context of PDEs
35K58 Semilinear parabolic equations
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