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Characterization of Turing diffusion-driven instability on evolving domains

journal contribution
posted on 2023-06-08, 11:20 authored by Georg Hetzer, Anotida Madzvamuse, Wenxian Shen
In this paper we establish a general theoretical framework for Turing diffusion-driven instability for reaction-diffusion systems on time-dependent evolving domains. The main result is that Turing diffusion-driven instability for reaction-diffusion systems on evolving domains is characterised by Lyapunov exponents of the evolution family associated with the linearised system (obtained by linearising the original system along a spatially independent solution). This framework allows for the inclusion of the analysis of the long-time behavior of the solutions of reaction-diffusion systems. Applications to two special types of evolving domains are considered: (i) time-dependent domains which evolve to a final limiting fixed domain and (ii) time-dependent domains which are eventually time periodic. Reaction-diffusion systems have been widely proposed as plausible mechanisms for pattern formation in morphogenesis.

History

Publication status

  • Published

Journal

Discrete and Continuous Dynamical Systems - Series A

ISSN

1078-0947

Publisher

American Institute of Mathematical Sciences

Issue

11

Volume

32

Page range

3975-4000

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2012-04-16

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