On the existence of two stationary solutions for a free boundary problem describing cell motility

Article Sidebar

PDF
Published: Mar 30, 2016
DOI: https://doi.org/10.5556/j.tkjm.47.2016.1889
Keywords:
Free boundary problems Cell crawling

Main Article Content

Harunori Monobe

Abstract

This paper is concerned with the existence of stationary solutions for a free boundary problem related to cell motility. In recent years, the author and Ninomiya \cite{monobe_ninomiya} showed that there exist at least two stationary solutions with disk-shaped domains in isotropic boundary conditions. In this paper, it will be shown that there exist exactly two stationary solutions for the free boundary problem under the same boundary conditions. The proof is based on the weak maximum principle and the mean-valued theorem.

Article Details

How to Cite
Monobe, H. (2016). On the existence of two stationary solutions for a free boundary problem describing cell motility. Tamkang Journal of Mathematics, 47(1). https://doi.org/10.5556/j.tkjm.47.2016.1889
Issue
Vol. 47 No. 1 (2016)
Section
Special Issue
Author Biography

Harunori Monobe

Meiji Institute ofMathematical SciencesMeiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, 164-8525, Japan.

References

D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, New York, 1998.

A. Mogilner and L. Edelstein-Keshet, Regulation of actin dynamics in rapidly moving cells, A quantitative analysis. Biophys. J., 83(2002), 1237—1258.

A. Mogilner, J. Stajic and C. W. Wolgemuth, Redundant mechanisms for stable cell locomotion revealed by minimal models, Biophys J., 101(2011), 545--553.

A. Mogilner and B. Rubinstein et al, Actin-myosin viscoelastic flow in the keratocyte lamellipod, Bio. J., 97(2009), 1853--1863.

H. Monobe, Behavior of solutions for a free boundary problem describing amoeba motion, Differential and Integral Equations, 25(2012), 93--116.

H. Monobe and H. Ninomiya, Multiple existence of traveling waves of a free boundary problem describing cell motility, Discrete and Continuous Dynamical Systems Series B, 19(2014),789--799.

J. V. Small, M. Herzog and K. Anderson, Actin filament organization in the fish keratocyte lamellipodium, J. Cell Biol., 129(1995), 1275--1286.