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Multiphase volumepreserving interface motions via localized signed distance vector scheme
Behavior of radially symmetric solutions for a free boundary problem related to cell motility
1.  Meiji Institute of Mathematical Sciences, Meiji University, 4211 Nakano, Nakanoku, Tokyo, 1648525 
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, Actinmyosin 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 1D 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 chemomechanical 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, Actinmyosin 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 1D 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 chemomechanical model for amoeboid cell movement,, (in preparation)., (). Google Scholar 
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