# American Institute of Mathematical Sciences

February  2017, 37(2): 905-914. doi: 10.3934/dcds.2017037

## Traveling wave solutions with convex domains for a free boundary problem

 1 Meiji Institute of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, 164-8525, Japan 2 School of Interdisciplinary Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, 164-8525, Japan

Received  March 2015 Revised  September 2015 Published  November 2016

Fund Project: The first author is partially supported by Grant-in-Aid for Research Activity Start-up (No. 20635809) from the Japan Society for the Promotion of Science. The second author is partially supported by Grant-in-Aid for Scientific Research (B) (No. 26287024) from the Japan Society for the Promotion of Science

In this paper, a free boundary problem related to cell motility is discussed. This free boundary problem consists of an interface equation for the domain evolution and a parabolic equation governing actin concentration in the domain. In [10] the existence of traveling wave solutions with disk-shaped domains were shown in a special situation where a polymerization rate is specified. In this paper, by relaxing the condition for the polymerization rate, the previous result is extended to the existence of traveling wave solutions with convex domains.

Citation: Harunori Monobe, Hirokazu Ninomiya. Traveling wave solutions with convex domains for a free boundary problem. Discrete & Continuous Dynamical Systems - A, 2017, 37 (2) : 905-914. doi: 10.3934/dcds.2017037
##### References:

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##### References:
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