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Infinite Dimensional Dynamical Systems pp 119–140Cite as

Instability of Radially-Symmetric Spikes in Systems with a Conserved Quantity

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Part of the book series: Fields Institute Communications ((FIC,volume 64))

Abstract

We show that radially symmetric spikes are unstable in a class of reaction-diffusion equations coupled to a conservation law.

Mathematics Subject Classification (2010): Primary 37L15; Secondary 35L65

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Notes

  1. 1.

    Here, Iαand Kαare the modified Bessel functions satisfying the equation\({r}^{2}h^{\prime\prime} + rh - ({r}^{2} + {\alpha }^{2})h = 0\), such that Kαis bounded at ∞, Iαis bounded at 0, see [9].

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Acknowledgements

The authors gratefully acknowledge support by the National Science Foundation under grant NSF-DMS-0806614.

Received 1/9/2010; Accepted 6/27/2010

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota, 206 Church St. S.E., Minneapolis, MN, 55455, USA

    Alin Pogan & Arnd Scheel

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  1. Alin Pogan
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  2. Arnd Scheel
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Correspondence to Alin Pogan .

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Editors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, USA

    John Mallet-Paret

  2. Department of Mathematics and Statistics, York University, Toronto, ON, Canada

    Jianhong Wu  & Huaiping Zhu  & 

  3. Georgia Institute of Technology, School of Mathematics, Atlanta, GA, USA

    Yingfei Yi

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Pogan, A., Scheel, A. (2013). Instability of Radially-Symmetric Spikes in Systems with a Conserved Quantity. In: Mallet-Paret, J., Wu, J., Yi, Y., Zhu, H. (eds) Infinite Dimensional Dynamical Systems. Fields Institute Communications, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4523-4_4

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