Multiple existence of traveling waves of a free boundary problem describing cell motility
Harunori Monobe, Hirokazu Ninomiya · Discrete and Continuous Dynamical Systems - B · 2014
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 problemfor a continuous map $T$ and then show that there exist at least two fixed pointsfor the map $T$.