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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

Harunori Monobe 1,

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.
Keywords: Free boundary problems, cell crawling..
Mathematics Subject Classification: Primary: 35R35; Secondary: 92C1.
Citation: Harunori Monobe. Behavior of radially symmetric solutions for a free boundary problem related to cell motility. Discrete & 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, (1996).  doi: 10.1142/3302.  Google Scholar

[2]

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

[3]

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

[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.   Google Scholar

[5]

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

[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.  doi: 10.3934/dcdsb.2014.19.789.  Google Scholar

[7]

T. Umeda, A chemo-mechanical model for amoeboid cell movement,, (in preparation)., ().   Google Scholar

show all references

References:
[1]

G. M. Lieberman, Second Order Parabolic Differential Equations,, World. Scientific, (1996).  doi: 10.1142/3302.  Google Scholar

[2]

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

[3]

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

[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.   Google Scholar

[5]

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

[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.  doi: 10.3934/dcdsb.2014.19.789.  Google Scholar

[7]

T. Umeda, A chemo-mechanical model for amoeboid cell movement,, (in preparation)., ().   Google Scholar

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