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A construction of patterns with many critical points on topological tori

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Abstract

We consider reaction–diffusion equations on closed surfaces in \({{\mathbb {R}}}^3\) having genus 1. Stable nonconstant stationary solutions are often called patterns. The purpose of this paper is to construct closed surfaces together with patterns having as many critical points as one wants.

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Authors and Affiliations

  1. Research Center for Pure and Applied Mathematics, Graduate School of Information Sciences, Tohoku University, Sendai, 980-8579, Japan

    Putri Zahra Kamalia & Shigeru Sakaguchi

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  1. Putri Zahra Kamalia
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  2. Shigeru Sakaguchi
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Correspondence to Putri Zahra Kamalia.

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This research was partially supported by the Grant-in-Aid for Scientific Research (B) (\(\sharp \) 18H01126) of Japan Society for the Promotion of Science.

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Kamalia, P.Z., Sakaguchi, S. A construction of patterns with many critical points on topological tori. Nonlinear Differ. Equ. Appl. 27, 39 (2020). https://doi.org/10.1007/s00030-020-00643-x

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  • DOI: https://doi.org/10.1007/s00030-020-00643-x

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