Global existence for semilinear reaction-diffusion systems on evolving domains

Details Global existence for semilinear reaction-diffusion systems on evolving domains Global existence for semilinear reaction-diffusion systems on evolving domains

2010-05-25

arxiv.org/abs/1005.4493v3

Journal of Mathematical Biology online first 4 Feb 2011

Nonlinear Sciences

Pattern Formation and Solitons

24 pages, 3 figures

Scientific paper

10.1007/s00285-011-0404-x

We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that commonly arise in the theory of pattern formation. We present numerical results illustrating our theoretical findings.

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