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Multiple existence of traveling waves of a free boundary problem describing cell motility

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  • In this paper we consider a free boundary problem describing cell motility, which is a simple model of Umeda (see [11]). This model includes a non-local term and the interface equation with curvature. We prove that there exist at least two traveling waves of the model. First, we rewrite the problem into a fixed-point problem for a continuous map $T$ and then show that there exist at least two fixed points for the map $T$.
    Mathematics Subject Classification: Primary: 35C07, 35R35; Secondary: 92C17.


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