Article Contents
Article Contents

Traveling wave solutions with convex domains for a free boundary problem

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.

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

 Citation:

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