Characterization of Turing diffusion-driven instability on evolving domains

Hetzer, Georg, Madzvamuse, Anotida and Shen, Wenxian (2012) Characterization of Turing diffusion-driven instability on evolving domains. Discrete and Continuous Dynamical Systems - Series A, 32 (11). pp. 3975-4000. ISSN 1078-0947

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: Anotida Madzvamuse
Date Deposited: 16 Apr 2012 09:27
Last Modified: 10 Mar 2017 12:02
URI: http://sro.sussex.ac.uk/id/eprint/38656

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