TY - JOUR
T1 - Traveling wave solutions with convex domains for a free boundary problem
AU - Monobe, Harunori
AU - Ninomiya, Hirokazu
N1 - Funding Information:
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.
Publisher Copyright:
© 2017, Southwest Missouri State University. All rights reserved.
PY - 2017/2
Y1 - 2017/2
N2 - 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.
AB - 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.
KW - Cell crawling
KW - Free boundary problems
KW - Traveling waves
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U2 - 10.3934/dcds.2017037
DO - 10.3934/dcds.2017037
M3 - Article
AN - SCOPUS:85006339864
SN - 1078-0947
VL - 37
SP - 905
EP - 914
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
IS - 2
ER -