Anchored spirals in the driven curvature flow approximation

Author:

Nan Li, Arnd Scheel

Keyword:

Nonlinear Sciences, Pattern Formation and Solitons, Pattern Formation and Solitons (nlin.PS), Analysis of PDEs (math.AP)

journal:

date:

2023-12-13 00:00:00

Abstract

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. \end{abstract}

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