Instability of anchored spirals in geometric flows

2025/04/09 by Anthony Cortez, Nan Li, Cortez, Anthony +9 · 1 voice
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS) #math.AP #nlin.PS

paper · pdf · doi:10.48550/arxiv.2504.07270

arxiv published 2025/04/09 · arxiv updated 2026/02/05

Abstract

We investigate existence, stability, and instability of anchored rotating spiral waves in a model for geometric curve evolution. We find existence in a parameter regime limiting on a purely eikonal curve evolution. We study stability and instability theoretically, in the aforementioned limiting regime, and numerically. We find convective and absolute oscillatory instability, as well as saddle-node bifurcations. Our results in particular shed light on the instability of spiral waves in reaction-diffusion systems caused by an instability of wave trains against transverse modulations.

Discussions

• Anthony Cortez, Nan Li, Nathan Mihm, Alice Xu, Xiaoxing Yu, Arnd Scheel: Instability of anchored spirals in geometric flows https://arxiv.org/abs/2504.07270 https://arxiv.org/pdf/2504.07270 https://ar [bsky, 0 points, 1 comments]

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