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Existence of Spikes for the Shadow Gierer-Meinhardt System

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Book cover Mathematical Aspects of Pattern Formation in Biological Systems

Part of the book series: Applied Mathematical Sciences ((AMS,volume 189))

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Abstract

We study the existence of boundary spikes for the shadow Gierer-Meinhardt system in higher dimensions. We use Liapunov-Schmidt reduction and the Localised Energy Method in combination with geometric computations depending on the neighbourhood of the spike.

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Authors and Affiliations

  1. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China

    Juncheng Wei

  2. Department of Mathematical Sciences, Brunel University, Uxbridge, UK

    Matthias Winter

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  1. Juncheng Wei
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  2. Matthias Winter
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Wei, J., Winter, M. (2014). Existence of Spikes for the Shadow Gierer-Meinhardt System. In: Mathematical Aspects of Pattern Formation in Biological Systems. Applied Mathematical Sciences, vol 189. Springer, London. https://doi.org/10.1007/978-1-4471-5526-3_5

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