Traveling wave solutions with convex domains for a free boundary problem

Harunori Monobe; Hirokazu Ninomiya

doi:10.3934/dcds.2017037

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2017, Volume 37, Issue 2: 905-914. Doi: 10.3934/dcds.2017037

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Traveling wave solutions with convex domains for a free boundary problem

Harunori Monobe^1, and
Hirokazu Ninomiya^2,

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

Author Bio: E-mail address: te12001@meiji.ac.jp; E-mail address: hirokazu.ninomiya@gmail.com

Received: March 2015

Revised: September 2015

Published: May 2017

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.

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Abstract

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.

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Mathematics Subject Classification: Primary:35C07, 35R35;Secondary:92C17.

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References

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