Classification of Steadily Rotating Spiral Waves for the Kinematic Model
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abstract

Spiral waves arise in many biological, chemical, and physiological systems.
The kinematical model can be used to describe the motion of the spiral arms
approximated as curves in the plane. For this model, there appeared some
results in the literature. However, these results all are based upon some
simplification on the model or prior phenomenological assumptions on the
solutions. In this paper, we use really full kinematic model to classify a
generic kind of steadily rotating spiral waves, i.e., with positive (or
negative) curvature. In fact, using our results (Theorem 8), we can answer the
following questions: Is there any steadily rotating spiral wave for a given
weakly excitable medium? If yes, what kind of information we can know about
these spiral waves? e.g., the tip's curvature, the tip's tangential velocity,
and the rotating frequency. Comparing our results with previous ones in the
literature, there are some differences between them. There are only solutions
with monotonous curvatures via simplified model but full model admits solutions
with any given oscillating number of the curvatures.