# American Institute of Mathematical Sciences

October  2015, 8(5): 989-997. doi: 10.3934/dcdss.2015.8.989

## Behavior of radially symmetric solutions for a free boundary problem related to cell motility

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

Received  December 2013 Revised  June 2014 Published  July 2015

We consider a free boundary problem related to cell motility. In the previous work, the author [5] replaced the boundary condition, in the original problem, with a simple boundary condition and studied the behavior of radially symmetric solutions for the modified problem. In this paper, we consider the original mathematical model and show that the behavior of solutions for the model is similar to the one of solutions for the modified model under the certain condition.
Citation: Harunori Monobe. Behavior of radially symmetric solutions for a free boundary problem related to cell motility. Discrete and Continuous Dynamical Systems - S, 2015, 8 (5) : 989-997. doi: 10.3934/dcdss.2015.8.989
##### References:
 [1] G. M. Lieberman, Second Order Parabolic Differential Equations, World. Scientific, Publishing Co., Inc., River Edge, N.J., 1996. doi: 10.1142/3302. [2] A. Mogilner and B. Rubinstein et al, Actin-myosin viscoelastic flow in the keratocyte lamellipod, Bio. J., 97 (2009), 1853-1863. [3] A. Mogilner, J. Stajic and C. W. Wolgemuth, Redundant mechanisms for stable cell locomotion revealed by minimal models, Biophys J., 101 (2011), 545-553. [4] A. Mogilner and D. W. Verzi, A simple 1-D physical model for the crawling nematode sperm cell, J. Stat. Phys., 110 (2003), 1169-1189. [5] H. Monobe, Behavior of solutions for a free boundary problem describing amoeba motion, Differential and Integral Equations, 25 (2012), 93-116. [6] H. Monobe and N. Hirokazu, Multiple existence of traveling waves of a free boundary problem describing cell motility, Discrete Contin. Dyn. Syst., 19 (2014), 789-799. doi: 10.3934/dcdsb.2014.19.789. [7] T. Umeda, A chemo-mechanical model for amoeboid cell movement,, (in preparation)., ().

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##### References:
 [1] G. M. Lieberman, Second Order Parabolic Differential Equations, World. Scientific, Publishing Co., Inc., River Edge, N.J., 1996. doi: 10.1142/3302. [2] A. Mogilner and B. Rubinstein et al, Actin-myosin viscoelastic flow in the keratocyte lamellipod, Bio. J., 97 (2009), 1853-1863. [3] A. Mogilner, J. Stajic and C. W. Wolgemuth, Redundant mechanisms for stable cell locomotion revealed by minimal models, Biophys J., 101 (2011), 545-553. [4] A. Mogilner and D. W. Verzi, A simple 1-D physical model for the crawling nematode sperm cell, J. Stat. Phys., 110 (2003), 1169-1189. [5] H. Monobe, Behavior of solutions for a free boundary problem describing amoeba motion, Differential and Integral Equations, 25 (2012), 93-116. [6] H. Monobe and N. Hirokazu, Multiple existence of traveling waves of a free boundary problem describing cell motility, Discrete Contin. Dyn. Syst., 19 (2014), 789-799. doi: 10.3934/dcdsb.2014.19.789. [7] T. Umeda, A chemo-mechanical model for amoeboid cell movement,, (in preparation)., ().
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