2023/12/13 by Nan Li, Li, Nan, Arnd Scheel +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geomagnetism and Paleomagnetism Studies #Geometric Analysis and Curvature Flows #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2312.07809
openalex publication_date 2023/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study existence, asymptotics, and stability of spiral waves in a driven curvature approximation, supplemented with an anchoring condition on a circle of finite radius. We analyze the motion of curves written as graphs in polar coordinates, finding spiral waves as rigidly rotating shapes. The existence analysis reduces to a planar ODE and asymptotics are given through center manifold expansions. In the limit of a large core, we find rotation frequencies and corrections starting form a problem without curvature corrections. Finally, we demonstrate orbital stability of spiral waves by exploiting a comparison principle inherent to curvature driven flow. \endabstract